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AN ECONOMIC ANALYSIS OF FARM REVENUE INSURANCE

By

David Dale Trechter

A DISSERTATION

Subnitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1984

0 Copyright by
DAVID DALE TRECHTER

1984

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ABSTRACT
AN ECONOMIC ANALYSIS OF FARM REVENUE INSURANCE

BY

David Dale Trechter

In the 1981 Farm Bill. Congress included a provision calling
for a study of the feasibility of replacing current farm income support
programs with a farm revenue insurance program. Purchase of a revenue
insurance policy would guarantee a farmer some minimum level of gross
receipts from his farm operation. The insurable level would be
determined from a farmer's average returns over a base period and would
adjust over time to reflect changing market conditions and inflation.
The program would not guarantee a level of net income nor would the
protection cover off-farm earnings.

Expected Value-Variance models of revenue insurance demand
and supply were developed. These models predict that as buyers become
more risk averse, face a higher premium. become less wealthy or. in
general. as the environment becomes more uncertain. the level of
insurance coverage sought will increase. A supply model is derived by
aggregating across buyers. A seller will offer higher levels of
coverage if he knows buyers have become more risk averse, if his own
risk aversion decreases or if there is a decline in the degree to which
his clients' outcomes are correlated.

A computer program was developed to examine the cost of and
farmer attitudes toward a revenue insurance program. Twenty farmers
were questioned about revenue insurance. Many farmers expressed

disinterest and skepticism about revenue insurance. Many felt the

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insurance premium would be expensive, record keeping burdonsome and
cheating rampant. Despite these initial reactions most farmers
indicated they would willingly pay a premium that would more than cover
the estimated indemnity costs of the program. Indemnities proved to be
much lower than anticipated. One explanation is the expected negative
correlation between prices and quantities. Another possibility is that
because tax data were used. stability of farm revenues was overstated.
A revenue insurance seems capable of drawing participants from farms of
all sizes. Younger farmers. in particular. seemed attracted to it.
Since cost and level of coverage are dependent upon the
management decisions of the individuals, revenue insurance could help
coordinate the food system by improving transmission of market signals

yet protect individual farms from unstable markets.

 

 

 

This dissertation is dedicated to my mother. Mary Trechter who suffered
through the birth of me. and to my wife. Kristen Allen. who suffered
through the birth of this dissertation.

ACKNOWLEDGEMENTS

There are many things about writing a dissertation that are
INJt fun. One of the things that Is fun is, having completed the task.
sitting back to thank all of the people who helped make it all
possible. Assistance comes in many forms. '

First. let me thank the Department of Agricultural Economics
for the variety of assistantships I was given. I am also very
appreciative of the United States Department of Agriculture who
provided the financial resources needed to carry out this study.

I would like to thank Dr. Robert Stevens, my major professor
during my coursework, for wise counsel and the occassional prod to meet
various academic deadlines. Both the counsel and the prods were
necessary and appreciated. Dr. James Shaffer. my major professor
during the thesis stage, and Dr. Lindon Robison, my thesis supervisor.
deserve more thanks than can be offered here. No one could ask for
better mentors. Both have forced me to stretch myself intellectually
which is what graduate school should be about.

Finally, for assistance in maintaining a semblance of
sanity, there are a number of people to whom I would like to express my
thanks, John Halloran and Becky Johnson, thanks for many enjoyable
hours on the basketball court. Thanks also to Margret and Wick for
Periodically providing a refuge from academia. I'm not sure that
acquiring the computer maintained or upset my sanity but thanks Mom for
the capital infusion none-the—less. Doug Krieger, thanks for building
'Y 830 on the squash court. Larry Lev and Ann Shriver. thanks for the
POt luck dinners and your friendship. Michael Morris thanks for
Walking G and A on those days when Kris and I didn't feel up to it and
for two years of easy living. To Carlos Vaccaro, thanks for long hours
0f philosophizing. Larry Cornell, thanks for the Fortran lessons,
you're a good mate. And most especially, thanks to Kris Allen, the
best: thing that happened to me at graduate school.

ii

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TABLE OF CONTENTS

Chapter 1

Introduction .

Public Policy in Agriculture and the

Rationale for Revenue Insurance
Revenue Insurance within this Conceptual Framework.
The Case for Revenue Insurance.
The Need for an Analysis of Revenue Insurance
Organization of the Dissertation.

Chapter 2

A Short History of Agricultural Insurance: Lessons for
the Design of a Revenue Insurance Program .

Crop Insurance in Other Countries

Crap Insurance in Canada .

Crop Insurance in Japan.

Crop Insurance in France .

Crop Insurance in Sweden . .
Conclusions Drawn from the Programs Discussed
Crop Insurance in the United States
The Current Crop Insurance Program .
Conclusions Drawn from the Experience of FCIC
The Prospective Revenue Insurance Program .

An Alternative Program Formulation

Justification of the Alternative Formulation

Chapter 3

A Summary of Empirical and Theoretical Studies of Insurance:

The Economic and Psychological Schools

The Economic Approach . . .
Theoretical Models of Insurance Purchases
Empirical Models of Insurance Purchases
Theoretical Models of Insurance Sales
Empirical Models of Insurance Sellers

The Psychological Approach . .

The Approach Used in this Study .

iii

Page

CDUIOONH

11
11
14
16
19
21
22
23
24
28
30
31

37

37
37
48
50
55
57
65

Chapter 4

Page
A Theoretical Model of Revenue Insurance Demand . . . . . . . 69
.An Expected Value-Variance Model . . . . .. . . . . . . . 69
1A Conceptual View of the Insurance Option . . . . . . . . . 72
A Mathematical Model of Insurance Demand . . . . . . . . . 76
Forming the Certainty Equivalent Expression . . .. . . . . 80
Conclusion . . . . .. . . . . . . .. . . . . . . . .. . 86
Chapter 5
A'Theoretical Model of Insurance Supply . . . . . . .. . . . 90
The Supply of Insurance . . . . . . . . . . . . . . . 90
.A Market Model of Revenue Insurance . . . . . . .. . . . . 91
A Mathematical Model of Insurance Supply . . . .. . . . . 94
The Expected Value-Variance Model for
the Insurance Seller . . . . . . . . . . . . . . . 97
Optimization in the Seller's Market . . . . . . . . . . . . 100
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 104
Chapter 6
An Empirical Test of the Theoretical Models . . . . . . . . . 107
The Empirical Model . . . . . . . . . . . . . . . . . . . . 107
The'Sample . . .. . . . . . . . .. . . . . . . . . .. . 119
TheData.........................120
Results . . . . . . . . . . . . .. . . . . . . . .. . . 123
Aggregate Results . . . . . . 180
The Effect of Increased Instability on Premium Costs . . 133
'flhe Aggregate Demand Curve . . . . . . . . . . . . . . . . 134
QuaIitative Assessment . . . . . . . . . . . . . . . . . . 138
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Chapter 7
Revenue Insurance in American Farm Policy . . . . . . . . . . 142
Farm Income Problems and Revenue Insurance . . . . 142
Instability in Agricultural Markets and Revenue Insurance . 148
The Business Cycle . . . . . . . . . . . . . . . . . . . 152
Foreign Trade . . . . . . . . . . . . . . 158
The Industrialization of Agriculture . . . . . . . . . . 165
Chronic Excess Supply . . . . . . . . . . . . . . . . . 167
Summary and Conclusions . . . . . . . . . . . . . . . . . 168

iv

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Chapter 8

Page
Summary. Conclusions and Issues for Further Research . . . . . 171
Summary . . . . . . . . . . . . . . . 171
An Evaluation of Revenue Insurance . . . . . . . . . . . . 173
Methodological Issues . . . . . . . . . . . . . . . 177
Revenue Insurance Program Issues . . . . . . . . . . . . 179
Appendices
Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . 182
Appendix 2 . . . . .. . . . . . . . . . . . .. . . . . . 184
Appendix 3 . . . . . . . . . . . . . . . . . . . . . . . . 185
Bibliography . . . . . . . . . . . . .. . . . . . . . . . . 189

6.5

6.6

6.7

6.8

LIST OF TABLES

Page
Characteristics of an Ideal Revenue Insurance Program
As Proposed by the Revenue Insurance Task Force . . . . . . 29
Summary of the Alternative Revenue Insurance Program . . . . 31
Summary of Viscusi's Comparative Statics Results . . . . . . 44
Two Lotteries . . . . . . . . . . . . . . . . . . . . . . . 62
The Effect of Changes in Model Variables on the Mean
and Variance of a Farmer's Insured Revenue PDF . . . . . . . 79
The Impact on the Optimal Level of Insurance of Changes
in the Factors Y2, , , . . . . . . . . . . . . . . . . . 82
Changes in Optimal Coverage Offerings with Changes
in Model Parameters . . . . . . . . . . . . . . . . . . . 101

“Two Hypothetical Choice Distributions for Use in Calculating

the Risk Aversion Coefficient of a Farmer. . . . . . . . . 113
Summary Description of Farms Visited . . . . . .. . . . . 120
Model Performance and Insurance Characteristics of the 15
Farms Studied. for 75 Percent Coverage . . . . . . . . . . 125
Comparison of Measured and Estimated Values for the

Loading Factor and Premium . . . . . . . . . . . . . . . . 131

Test of the Significance of Differences in the Loading
Factor and Premium Estimates Using Two

Estimation Techniques . . . . . . . . . . . . . . . . . . 132
Comparison of Measured and Estimated Values for the

Loading Factor and Premium When Alpha Doubles . . . . . . . 134
Participation Rates. Seller's Returns and Seller's

Surplus as Related to the Loading Factor . . . . . . . . . 136
The Proportion of Acreage Covered at Various

Loading Factor Levels . . . . . . . . . . . . . . . . . . 138

vi

7

7

7.

.1

.2

.3

4

Effect of Leverage on Refinancing (Percent)

Cyclical Movements in Per Capita Farm and
Non—Farm Income(a)

Cyclical Movements in Per Capita Farm and Non—Farm
Disposable Income (From All Sources)

Income from Off-farm Sources as a Percentage of Total

Income for Four Sizes of Farms. (Classes Based on
Value of Sales)

vii

Page

150

153

155

157

LIST OF FIGURES

Page
Comparison of Smith's and Jones' PDF . . . . . . . . . . . 27
Income and Substitution Effects for Insurance Purchases . 41
Insurance Offerings to Low and High Risk Buyers . . . . . 51
Disequilibrium in an Insurance Market with Two
Groups of Buyers . . . . . . . . . . . . . . . . . . . . . 53
The Value Function as Hypothesized by Prospect Theory . . 59
Equilibrium on an EV Frontier . . . . . . . . . . . . . . 70
The PDF with a Deductible Form of Insurance . . . . . . . 73
The PDF with the Coinsurance Form of Insurance . . . . . . 74
The Effect of Revenue Insurance for Farmer Jones . . . . . 75
A Mean Preserving Spread Holding P Constant . . '1' . . . 83
A Mean Preserving Spread. P and Y2 Increase. . . . . . . . . 85
A Mean Preserving Spread. P Decreases and Y2 Increases . . . 86
PDF of Seller's Revenue from a Given Buyer . . . . . . . . 92
The PDF of Returns to the Seller from Three Buyers . . . . 93
The PDFs of Two Buyers . . . . . . . . . . . . . . . . . . 96
The Effect on the Seller’s Revenue of a Shift in Buyer i's
PDF in which Y2 Increases and P Decreases . . . . . . . . 104
Part 1 of Computer Simulation Flow Chart - Data Entry
and PDF Estimation . . . . . . . . . . . . . . . . . . . . 110
Part 2 of Computer Simulation Flow Chart — Estimation of
the Farmer's Risk Aversion Coefficient . . . . . . . . . . 110
Part 3 of Computer Simulation Flow Chart
- Premium Estimation . . . . . . . . . . . . . . . . . . . 111

viii

 

6.4

6.5

6.6

6.7

6.8

Two Distributions Used to Locate Indifference Points
Choice Tree for Interval Approach to Risk Aversion
Coefficient Estimation

Participation as a Function of the Loading Factor

Expected Returns in a Revenue Insurance Program for
Different Loading Factors

Export Revenue as a Percentage of the Value of
Production for Wheat. Corn and Soybeans, 1951 - 1978(a)

ix

Page

113

117

135

136

149

Chapter 1:
Introduction

In the 1981 Farm Bill. Congress included a provision calling

upon the United State Department of Agriculture to study the concept of

far. revenue insurance as an alternative or supplement to the existing

set: of agricultural programs. The specific terms of the revenue
insurance program have not yet been determined but its intent is clear.

A revenue insurance policy seeks to offer the American farmer some

Protection from both economic and environmental events which adversely

affect his earning potential. This dissertation provides an economic
analysis of revenue insurance. Of particular concern is the
diatribution and level of the program's costs.
mlic Policy in Agriculture and the Rationale for Revenue Insurance

A useful way of thinking about agricultural policy is as a
8°C 1etal decision regarding the allocation of risks associated with
agl‘ iculture. A policy maker has a spectrum of policy choices
I‘egarding the allocation of risk bearing responsibilities. The options
beltlge from policies allocating all risk bearing costs to the farmer to

0‘)tions which allocate these costs to society as a whole.1

Risk, in this study. is defined as any uncertain outcome

which affects the well-being of a decision maker.2 Risks may result

tI‘om events in the physical environment (weather, pests or disease) or
I'tarket factors (institutional changes. political events. inflation.

Changes in consumer demand patterns. etc.). The characteristics of

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some types of hazards allow risk bearing responsibilities to be shifted
between individuals. For example. hail insurance is purchased by many
farmers. This allows them to shift part of the risk bearing

responsibilities for this environmental threat to the insurance

company. This option is available to farmers because. in insurance
parlance, the risk of hail damage can be successfully "pooled". Hence.
they are "insurable“. To be insurable implies that individuals in the

pool face risks that are not highly correlated in a positive way. there
are sufficient numbers of people in the pool to calculate accurately
the probability of loss in a given period and losses are accidental and
measurable.3 Many risks faced by agricultural producers do not conform
to all these prerequisites. "Indeed. the absence of adequate insurance
llalf‘kets has provided a significant part of the rationale for government
1rItervention, and particularly for government price stabilization
programs" in agriculture.4
We Insurance within this Conceptual Framework
Given this conceptual framework for agricultural policy. how
can the revenue insurance proposal be classified? With respect to the
E11 location of risk bearing. revenue insurance may at first appear to be
a Shift to greater reliance on private risk bearing. The validity of
t"‘18 impression depends entirely upon the form in which the program is
i‘Illemented. If revenue insurance follows the pattern of Federal All-
Risk Crop Insurance, where the administrative costs of the program are
bOrne entirely by the government and all policies sold by private
1“surance companies are re-insured with the federal government. the
Shift of responsibilities to the private sector may not be substantial.

If. on the other hand. options markets are instituted by the government

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allowing insurance companies to shift some of the market risks and no
subsidies or government re-insurance are offered. a significant shift
of risk bearing from the public to the private sector would be
observed. How the burden of risk would be allocated within the private
sector (between insurance companies. options markets and farmers) under
this scenario is unclear.

The Case for Revenue Insurance

The current administration is interested in revenue
insurance because it believes that wherever possible private
institutions should replace governmental ones. According to this view.
the function of the government. with respect to revenue insurance. is
to provide the institutional setting within which the private sector
can successfully pool the risks associated with agriculture. A
multitude of private institutions for transferring risk from one party
to another already exist and many feel these institutions are better
able to handle this function than are bureaucracies. Furthermore.
many believe that government policies. as now constructed. disrupt
agricultural markets. Decisions about the form and substance of
agricultural policies are the subject of intense speculation on the
part of market participants. Numerous instances of markets reacting to
expected or actual changes in policy could be cited. This is seen as
an unfortunate side effect of the current programs.

Related to these philosophical concerns are several economic
reasons for looking at the revenue insurance option. One is the
embarrassingly large stockpiles of grain and dairy products currently
held by the government. These stocks are believed to have an adverse

impact on agricultural markets because participants do not know when

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they might be used to influence market conditions. Revenue insurance
would remove the government as a major actor in the commodity buying
and storage business in the sense that this mechanism would no longer
be used for farm income protection. In addition, the rapidly
escalating cost of farm programs provides an impetus for examining the
revenue insurance proposal. Proponents of this policy believe it will
reduce government expenditures on behalf of agriculture. The
likelihood of this being the case depends upon the form such a program
takes.

At a microeconomic level. revenue insurance is seen as a way
of improving the planning efforts of farmers. By helping stabilize
farm revenue. revenue insurance would reduce financial uncertainties.
Assurance of a minimum level of revenue would help the farmer plan
investment decisions. particularly in longer lived investments such as
plant and equipment. Improved planning capacity could have important
consequences for the coordination and performance of the food system.
For instance, one macroeconomic manifestation of farm level
uncertainties is the phenomenon of cycles in the price of agricultural
commodities. Explanations of cycles are many (inaccurately framed
price expectations. efforts by the farmer to minimize tax payments by
investing in fixed assets in good years. an inelastic demand curve.
etc.). Revenue insurance may not directly affect the underlying causes
of cycles. but would reduce economic dislocations caused by them by
stabilizing gross receipts earned by the farm.

Finally, revenue insurance would allow the insurer to profit
from inter-farm variation of revenue experience. For example, the

preceding paragraph raised the issue of cycles in agricultural markets.

From an insurer's point of view, there are two aspects about cycles
that are interesting. First, it is unlikely that all cycles will be at
the same point in their oscillations in the same period. This means
that by insuring a cross section of farm types. the insurance company
can use these cycles to its advantage in the sense of reducing
variations of indemnity outlays. Second. even within a given type of
output. there will be variations about the mean. Tracking the hog
cycle entails the plotting of average prices received on a given day
over a period of time. Within this average figure are individuals who
experience prices on either side of the mean. Some of these
individuals will receive high prices and no indemnity. In short. it is
not expected that the revenue experience of farms producing a given
type of output to be perfectly correlated. Furthermore. when
considered across different types of output. the likelihood of positive

correlation is further reduced.

Ihg_!eegrforvgniAnglysis of Revenue Insurance

There are at least three significant differences between use
of revenue insurance as the principal policy tool and current policy
efforts. First, revenue insurance seeks to stabilize revenue rather
than prices or quantities. Virtually all previous policy efforts to
protect farm income have tried to manage the quantity of agricultural
products produced or marketed (ie. land set asides. stockpiles,
marketing orders, etc). the quantity of products demanded (P.L. 480.
food stamps. etc.) or the price received by the farmer (ie. price
supports. deficiency payments and non-recourse loans). Both prices and

quantities are instrumental variables on the variable in which the

farmer is ultimately interested. income or profits. Revenue insurance
is focused more directly on a variable of concern than are current
programs. As a result. revenue insurance represents a major change in
the direction of policy.

Revenue insurance may also shift the incidence of risk
bearing. The degree to which revenue insurance changes the existing
distribution of risk bearing responsibilities depends largely upon the
specific provisions of the policy. Finally. regardless of the final
incidence of risk bearing. a revenue insurance program would shift
implementation from public to private institutions.

Any time significant policy changes are contemplated. the
degree of uncertainty in the food system is increased. There is
uncertainty about the cost of the program. how it might be implemented.
the distribution of costs and benefits. participant responses to their

altered choice set and so on.

.Qgganiggtion of the Dissertation

The next chapter provides an historical perspective of the
experience several countries. including the U.S.. have had with
agricultural insurance. This chapter also provides a more detailed
description of the specific provisions assumed for the revenue
insurance program. Chapter 3 reviews the insurance literature in the
disciplines of economics and psychology. This review will include both
theoretical models and empirical investigations of insurance markets.

In chapters 4 and 5 theoretical models of a revenue
insurance market are developed. Chapter 4 derives a microeconomic
model of revenue insurance demand. The principal reason for building

the microeconomic model is to understand likely farmer responses to

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revenue insurance and focus attention on factors that may determine the
degree of success a revenue insurance program will have. Chapter 5
tackles the difficult task of building an aggregate model from farm
level results. The aggregate model is needed to gain insights into
some of the program design questions which will have to be answered by
a policy maker considering a revenue insurance program. These models
also provide equations for participation rates and insurance costs as a
function of the buyers probability density function over revenue. and
the risk aversion characteristics of the participants.

Chapter 6 reports the results of empirical work examining
revenue insurance demand. Conclusions about revenue insurance based on
the empirical evidence are offered.

The seventh chapter examines in a more general way the
effect of a revenue insurance program on some of the problems facing
U.S. agriculture in the 19803. Based upon the results obtained in the
earlier chapters. the impact of a revenue insurance program on
agricultural production. the structure of the farming sector and farm
incomes will be examined. The eighth chapter will summarize the

conclusions reached and indicate directions for future research.

I am grateful to Dr. Kenneth Clayton U.S.D.A. for framing the issue
in this manner for me.

Lindon Robison and Bev Fleisher. 1984. p. 10.
Green. Mark R.. 1977, p. 49.

Newbery. David M.G. and Joseph E. Stigiitz, 1981, p. 8.

Ia

Chapter 2

A Short History of Agricultural Insurance:
Lessons for the Design of a Revenue Insurance Program
The motivation for a review of agricultural insurance is to
obtain a broader perspective from which to analyze revenue insurance.
Such a review can point out flaws in the design of earlier programs as

well as characteristics that have been important in successful ones.

There are two main types of agricultural insurance, single
and multiple peril coverage. Single peril coverage offers protection
from single hazard while multiple peril affords protection from
several. Hail and fire insurance are the most familiar types of single
peril coverage. Private companies have covered these hazards because
they conform to the prerequisites for insurability discussed in Chapter
1. Specifically, weather data are plentiful. it is relatively easy to
measure losses. these risks are not highly correlated across farms and
losses are accidental since farmers' actions have little affect on the
weather experienced.

Multiple peril crop insurance has also been available for
many years in some countries. Public institutions. such as the Federal
Crop Insurance Corporation. have been much more involved in multiple
peril insurance than is the case with hail or fire insurance. The
reasons private insurers are generally not involved in multiple peril

crop insurance are often couched in terms of an inability to develop a

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sufficiently broad insurance pool. What seems more probable is that
lack of data. an inadequate understanding of the complex interactions
of the large number of environmental factors which affect yields. and
the important role played by managerial decisions in the ultimate
outcome. prevent an actuarial assessment of such risks. For example.
the degree to which pests affect the yield of a crop is dependent upon
a large number of environmental factors: the amount and timing of
rainfall, atmospheric humidity. temperature. populations of insects and
organisms which prey on the.pest. the specific crop planted and so on.
There is not a complete understanding of all the interactions between
these factors. Furthermore. these environmental interactions are
profoundly affected by a farmer's management decisions: the pest
management system employed. use (or not) of irrigation. type of
irrigation used. timing of planting. etc.

Because of the complexity of multiple peril insurance. there
13 greater public sector involvement. Revenue insurance is a type of
mmZiple peril insurance. The list of hazards covered is simply
extended to include market risks. Adding complexity to a system that
13 already but poorly understood leads to the conclusion that the
public sector will surely be involved in a revenue insurance program.
Because of the government's involvement, experience with multiple peril
Crop insurance is likely to be more instructive to an understanding of
I“’"emie insurance than is the history of single peril instruments.
Thel‘efore, this review will concentrate exclusively on the record of
‘ultiple peril insurance. First. the experience of other countries
with crop insurance is examined. This will be followed by an

e"‘aiination of the history of crop insurance in the U.S.. The final

11

part of the chapter looks at revenue insurance: what it is, how it

might be structured. its goals and how it might work in the U.S.

Grog Insurance in Other Countries

A number of countries have experimented with various forms
of crop insurance.1 The crop insurance programs of Canada. Japan,
France. Sweden and the United States will be discussed. This choice
is dictated by the availability of information and the interesting

insights and lessons offered by the history of each.

Crop Insurance in Canada

The Prairie Farm Assistance Act (PFAA) of 1939 was the first
effort undertaken by the Canadian government in the area of crop
insurance. This program gave limited protection to producers of grain
in the wheat producing provinces of Western Canada but provided no
Protection to farmers producing other crops or to grain producers in
Other regions. The PFAA assessed a one percent levy on all grain
.arketed via the Canadian Wheat Board. Indemnities were paid whenever
Yields in a township fell below a given level. If yields in a township
t'911 below the guaranteed level. all producers living in that township
who grew that crop received an indemnity. The maximum amount any
Ii’at‘mer could receive from PFAA was $800.00 per year.2

A much more ambitious program was launched in 1959 under the
Federal Crop Insurance Act (FCIA). FCIA enables the federal government
to enter into an agreement with a province to help provide crop
ins“Pence. Currently. the federal government will pay up to 50 percent

of tZhe administrative expenses of the crop insurance program, they will

Subsidize the premiums paid by farmers by up to 25 percent and they

12

offer reinsurance services to the provinces.3 Insurable crops include
wheat, oats, barley, flaxseed, rye, seed corn. buckwheat, soybeans,
potatoes, sugar beets. tobacco, sunflower. rapeseed, apples. plums,
pears and apricots. These crops are insured against all natural
perils. As each provincial policy is unique. this discussion will
focus on the crop insurance program in Manitoba.

Manitoba was the first province to accept the federal
government's offer to assist in setting up a crop insurance program.
Less than two months after the federal enabling legislation was passed.
Manitoba began a pilot program in crop insurance. In its first year
Of operation. 1960. the Manitoba program attracted more than 38 percent

4 The Manitoba program offers crop insurance

of the eligible farmers.
in any area where at least twenty-five percent of the farmers who own
at least twenty-five percent of the cropped acreage indicate a
Willingness to participate in the program. Coverage is available at 50
percent. 60 percent and 70 percent of long term average yields. The
10118 term average yield may be established on the yields of the
individual farm or on the yields of all farms in the area in which the
farm is located. The farmer also has price elections (which set the
rate per bushel at which any compensation will be paid) to choose from.
Prellums are based on the productivity and riskiness of the area and
are Subsidized by the federal government. Twa other premium discounts
are available. One, called an experience discount. rewards growers
Who have made no claims on their policy. The second is a size discount
which lowers the premium by 5 percent when the insured acreage is 300

aCres or more. 5

The Canadian program has enjoyed a measure of success. It

13

has attracted a relatively large proportion of the eligible farmers and
has had a solid loss ratio, indemnities divided by premiums, of .88
over the years 1960 - 1975 when all provincial programs are taken as a
whole.6 Ray credits the success of the Canadian program to seven
factors:

1. The provinces were given the initiative to start and run programs.

2. The federal government covered the cost of administration and a
portion of the premium.

3. Crop insurance was the only form of disaster relief available to
farmers in areas where it was offered.

4. Coverage increased over time with the rate of inflation and the
cost of production.

5. Yields and coverage based on the experience of the individual
farmers were used as much as possible.

6. Efforts were made to coordinate public. all-risk crop insurance
and hail insurance to minimize duplication of coverage.

7. Good coordination with farmers needs and concerns was sought.7

The Canadian system is interesting because the program is
run and structured. in large measure. by the individual Provinces.
This is beneficial to the extent that programs can be tailored more
closely to the individual needs of the farming communities within each
province. However. it could lead to inequities across provinces. The
Federal government. by coordinating and overseeing all agricultural
insurance programs. seems to have minimized this problem.

Mention should also be made of another Canadian program
aimed at stabilizing returns to farming, the Western Grain
Stabilization Plan (WGSP). The WGSP covers wheat. oats. barley. rye.
flaxseed and rapeseed. It guarantees that net cash flows to the region

from sales made by the Canadian Wheat Board of the six crops mentioned

14

above, will not be less than the average for the previous five years.
Net cash flows are defined as gross receipts less cash costs of
production. Participation in the program is voluntary. Each
participating farmer contributes two percent of the value of his sales
to the Canadian Wheat Board as a type of indemnity. The dollar amount
of these contributions determines his share of any benefits disbursed
by the WGSP. Both the indemnity and the premium are proportionate to
the amount of production and do not reflect differing exposure to risk.

across farms or crops.

Crop Insurance in Japan
The Japanese system was begun in 1938. The insurance covers

crop losses caused by frost. flood. drought. wind, snow. insects. bird.

wildlife and plant diseases. The minimum loss that must be suffered
prior to making a claim is 30 percent. The proportion of the loss
indemnified increases with the size of loss. For example. if between

30 percent and 40 percent of a farmer's crop is lost. he may apply for
an indemnity that will cover at most 5 percent of the loss. For a loss
of 90-100 percent. the indemnity will cover at most 50 percent.8

Participation in the program is mandatory for all but the smallest

farms.

There are three levels in the administration of the Japanese
system. At the local level is the agricultural cooperative. The
second level is composed of federations of local 000peratives. The

role of the federations is to coordinate communications between the
local and the national levels. At the national level representatives
of the cooperatives have an advisory/lobbying role with the national

insurance agency and the Ministry of Agriculture. The national

15

organization manages a special fund used to cover unusually large
losses.

The national government pays all the administrative expenses
at the national level and a portion at the prefectoral and local
levels. The government also pays a large proportion of the farmers
premium. Premiums are based on the record of claims made by the
cooperative as a whole over the previous 20 years.9 The government's
portion of the premium increases with the riskiness of the production
area.

An interesting feature of the Japanese system is that
premiums are constant across producers of a given crop in a given
cooperative. The insurable yield. on the other hand. is determined for
each plot of land with the maximum coverage being seventy-five percent
of the established average yield.

The Japanese system is highly structured yet power is quite
decentralized. A great deal of power is vested in the local
agricultural cooperatives which sell policies, inspect and estimate
reported losses. determine the average yield for each plot of land.
collect premiums and disburse indemnities.

The Japanese system has the advantage of a high degree of
farmer involvement in the operation of the program. The Japanese
system for adjusting claims is particularly interesting. Local farmers
who are well-respected members of the community determine losses and
indemnities. This may increase confidence that the program is not
being manipulated by an insurance company for its own profit.
Communication between client and seller would also be expected to be

facilitated in this institutional setting. This mechanism is also

16

likely to result in inequities across cooperatives. For example, the
rulings of the claims adjusters in one cooperative may be
substaintially more generous than those of a neighboring cooperative.
There are other aspects of the Japanese program that seem
counterproductive. In particular. the higher level of subsidization of
premiums in high risk areas would be expected to encourage production
in these areas. The explanation for this probably lies in the
political importance of the farm vote in Japan and upon the aim of
Japanese policy to achieve self sufficiency in food production.
Another aspect of the program that is unusual is the manner in which
premiums and level of coverage are calculated. It is unclear why
premiums are calculated on a cooperative wide basis and coverage levels
on a farm by farm basis when it appears that data exist for calculating

a premium based on the experiences of the individual farm.

Crop Insurance in France
The first disaster relief program for farmers was begun in

10 At intermittent periods since that time. France

1567 in France.
has tried programs of various sorts. From 1933 until 1942. for
example, a special fund to protect farmers from losses caused by hail.
frost. flood or hurricane was created. The system was halted because
of the disruptions and fiscal crises caused by World War Two. ' As
financial statements were not published. the performance of this
program is difficult to evaluate quantitatively. Millot. however.

cites five weaknesses of the program:

1. The indemnity calculation was complex and likely to be
misunderstood by the farmer clients.

2. The process for making a claim on the policy was lengthy

17

and cumbersome. It took an average of two years to settle
a claim which. on average, covered about fifteen percent
of the loss.
3. Coverage was limited to the four hazards noted above.
4. There were no background studies done prior to
implementation. 11
5. Solid financial backing was lacking.
Not until 1964 was a new system of crop insurance enacted.
The new plan created the "Central Bank for Reinsurance" (CCR), a
Guarantee Fund, a National Commission and local "committees of
experts". Within the CCR a committee composed of three members of the

Ministry of Economics and Finance and three from the Ministry of

Agriculture controlled investments made on behalf of the Guarantee

Fund.

The National Commission. composed of farmers. insurers. and
government administrators. was charged with data collection and
analysis, disaster prevention efforts, overseeing money in the

Guarantee Fund and managing the indemnification process.

The local committee of experts evaluated claims for
indemnities within their county. They advised the prefet, or head of
county government. who was responsible for transmitting claims to the
national commission. The local committee also suggested an amount to
be paid to farmers who had submitted claims.

Funding for the program came from a variety of sources.
Farmers paid a premium. the national government contributed an amount
that at least matched the amount raised via premiums. local governments
covered operating expenses and some revenues were generated from
investments when premiums exceeded indemnities. Despite the variety of

funding sources. funding was a problem in the early years of operation.

18

The premium was collected by adding a ten percent surcharge to a
farmer's fire insurance premium and adding five percent to premiums
paid by them for other types of insurance. This means of collection
was adopted because it was easy to administer.

The French system is best described as discretionary. For
example, it was felt that a list of perils covered would be too
limiting, so it was left to the discretion of the National Committee to
determine what constituted an indemnifiable loss. Another example
would be the manner in which indemnities were determined. The
National Committee decided how much it would give each county and
published its ruling in the "Official Journal". A farmer with an
outstanding claim then had twenty days in which to press his claim with
the responsible insurance company. The insurance company passed the
claim to the local expert committee who decided what proportion of the
claim to pay.

One of the attractions of the French system is its
remarkable degree of flexibility. The legislation authorizing the
program indicated the general purpose of the insurance plan but did not
dictate what should be deemed an insurable event or the rate at which
compensation was to be granted. This flexibility allowed the
administrators of the program to respond to new and unanticipated
events. However. this flexibility was also one of the major weaknesses
0f the program. Like the Japanese system. the descretionary powers
Vested in the local committee of experts resulted in claims adjustments
tfllat were inconsistent across departments. In addition. the

discretionary power of the national commission over the amount of

inxdemnities granted each county appears to be highly susceptible to

19

misuse and at a minimum would increase the uncertainty in the system.
There are a number of other problems with the French system.
The system of taxing existing insurance policies as a source of revenue
for the government's own program is counterproductive. By increasing
the tax on all forms of insurance farmers will reduce the amount of
insurance coverage purchased. As a result. revenues from premiums for
the multiple peril insurance fall yet farmers become more dependent
upon the government program for insurance protection. In operation. a
lack of funds coupled with increased demands on the program. led to
farmers' complaints about low levels of indemnification. the inability
of the program to fulfill all of the tasks assigned to it and inability
to extend the coverage offered. Furthermore, the system of
indemnification was slow. complex and bureaucratic. The average
elapsed time between a report of damage and receipt of an indemnity was

2 The amount of compensation was small

estimated to be seven months.1
relative to the losses experienced. The law specified that the maximum
proportion of a loss that could be compensated was 75 percent. Between
1966 and 1968 the proportion of loss covered by insurance was between

ten and thirty-five percent.13

Crop Insurance in Sweden
In the Swedish system. begun in 1961. the basic unit of
analysis is not the farm but the agricultural district. of which there
are 400. The districts are drawn so as to contain as uniform a group of
farmers as possible. Twenty-four district agricultural boards verify
Yields. determine premiums and pay indemnities to the agricultural

districts under their sway. At the national level the administrative

20

authority is the National Agricultural Marketing Board.

The government pays all administrative costs and two-thirds
of the premiums. The remaining one—third is collected via taxes on
crops marketed by agricultural cooperatives. For farmers with more
than two hectares under cultivation. insurance is compulsory.

Compensation is based on the total value of output of a
given crop for an entire district. If this total value is less than the
value based on average yields then an indemnity is paid. This is
similar to the Western Grain Stabilization Plan of Canada. Such a

system is possible because all farm products are marketed by local

cooperatives.
Coverage is offered for wheat, barley. rye, oats.
oilseeds. potatoes and sugar beets. In addition, four year contracts

are offered on livestock by the Scandinavian Livestock Insurance
Company. In all cases the insurance is multiple peril.

The Swedish system. which pays benefits based on averages
for the agricultural district seems unlikely to be either an equitable
or an efficient way of providing protection from the risks faced by
farmers. Such a system produces the anomalous result that a farmer in a
given district could experience an above average year yet receive an
indemnity if his fellows in the district had sub-par years.
Furthermore. even if the agricultural districts are initially drawn to
ensure the maximum degree of homogeneity possible. it seems unlikely
that this is wholly achieved. This is even more unlikely when
considered in a dynamic context. This being the case. the insurance
needs of farmers in the district are likely to be different. The lack

of a direct connection between individual actions and rewards

21

(indemnities and premiums) is unlikely to provide the sort of

performance a policy maker is after.

Conclusions Drawn from the Programs Discussed
The conclusions drawn from these brief historical sketches
are that chances for a successful insurance program are enhanced when
policies reflect the individual farmer's experience as directly as
possible. when the terms of the policy are clearly enunciated. when
claims are adjudicated and settled promptly and when there are few (no)
close substitutes for the type of protection offered by the public
insurance program. In particular. it is important to link the cost of
protection to farm management decisions that influence exposure to
risk.
Having seen how systems in other countries work. the next

item of business is to examine the U.S. system of crop insurance.

22

Crop71nsurance in the United States
Several comprehensive histories of crop insurance in the
U.S. already exist and interested readers are directed to them for

14 The intent of this

further information regarding this program.
section is to summarize the current program and the performance
implications of some of its key components.

Crop insurance contracts are available in 1.526 of the 3.077
counties in the United States. Claims have been paid on losses
resulting from 119 different causes. Drought has been the most
frequently cited cause of loss. accounting for 41.5 percent of all
claims paid. Other losses covered by FCIC and the frequency of
occurrence include excess moisture (15.9 percent of claims). frost
(13.9 percent). hail (10.9 percent). wind (6.7 percent). insects (4.6
percent). disease (2.8 percent). flood (2.2 percent) and all other (1.6

15 Proponents of the crop insurance program argue that by

percent).
helping to insure a minimum level of output. it facilitates forward
contracting. access to credit. capital formation and investment
decisions.

In the following pages the U.S. crop insurance program will
be examined. Crop insurance is more like revenue insurance than any
program with which the U.S. has had experience. There are, however.
important differences between the two programs. The most obvious is
that revenue insurance would insure the combined price and yield
distributions rather than yields alone. Nevertheless. the experience

with crop insurance is likely to yield valuable lessons to anyone

interested in a revenue insurance program.

23

The Current Cropglnsurance Program

In 1980 several important amendments were made to previous
legislation regarding crop insurance. The most important change made
in 1980 was with respect to FCIC's mandate. In 1980 it was decided
that all-risk crop insurance would replace disaster payments as the
main form of disaster relief in U.S. agriculture. Starting in 1974 and
lasting until 1981 the federal crop insurance program was in direct
competition with the disaster payment program. Disaster payments were
available for most grains and cotton. They were. from the farmers'
point of view, the perfect insurance policy. one in which no premiums
were charged yet indemnities were substantial. Because of budgetary
constraints and what was perceived by many as the inequity of the
disaster payment system. the program was halted in 1981. Crop
insurance was to pick up the slack. The expanded role of crop
insurance was emphasized by the goal of FCIC to insure 60 percent of
eligible acreage by 1984.16

Prior to 1980 FCIC all-risk crop insurance had been sold by
Agricultural Stabilization and Conservation Service (ASCS) field
offices. Since then. all sales of crop insurance have been handled by
private insurance companies who reinsure all policies with FCIC.

An important 1980 reform was the expanded use of the
Individual Yield Coverage (IYC) plan. Under this plan a farmer who
wishes to have his coverage based on his actual historical experience
may do so by submitting three years of verifiable yield data from his
farm. This is averaged with seven years of county data to determine

the average yield for the farm and the insured yield. Each subsequent

24

year in which that crop is grown. a year of farm data is added to the
formula and a year of county data removed. After seven years. the
average yield calculation is based entirely on the farmer's
experiences.

A farmer wishing to purchase crop insurance must sign up
early in the cropping cycle. Generally. a contract must be signed by
the end of April. The contract will specify dates by which various
farming activities must be completed and acreage reports filed. For
instance. grain corn in Michigan has to be planted no later than June
10 and harvested no later than December 10 for the policy to be valid.
These dates may be relaxed by FCIC in the advent of unusual conditions.
Having planted his corn. the farmer must inform FCIC by June 30 how
many acres are involved in a given contract. If the farmer wants to
cancel an existing policy he must inform FCIC by December 31 of this

intent. otherwise. the policy is automatically renewed.

Conclgsionsigggwn from the Experiences of FCIC

The FCIC program has not been without problems. Probably
its most significant problem has been with participation rates. In
some areas. particularly the wheat producing states on the High Plains
and dry land cotton areas in Texas. participation rates have been high.
In large parts of the Corn Belt, on the other hand, participation is
almost nonexistent. In the Corn Belt, better managers tend not to
buy crop insurance because it offers them little protection. The
level of protection offered could be low for at least two reasons.
First, management and/or environmental factors are such that a decline

in yields sufficiently large to trigger the insurance policy is very

25

unlikely. Secondly. the reliance upon county averages in determining
the level of protection adversely affects the better than average
producer. For example. suppose the average yield for corn grown on
first quality land is 100 bushels per acre in county X. A policy
guaranteeing 75 percent of average yields guarantees an average farmer
that if his yields fall 25 percent or more below his average yields he
will receive compensation from FCIC. For an above average producer
whose average yield is 125 bushels per acre, yields would have to fall
40 percent below his average to be entitled to an indemnity from FCIC.
The result. many believe. is that FCIC suffers from an
adverse selection problem in the Corn Belt. Farmers. at least. seem to
believe participants in the program are farms with lower quality land

17 An indication of this is that Production Credit

and management.
Associations require some of their higher risk clients to purchase a
crop insurance policy as a prerequisite for a loan.

A significant difference between the actual average yield of
an above average farmer and the yield ASCS has established for his farm
could occur either because he has failed to report his yields to the
ASCS office each year or because the quality of his land is
significantly better than classified by ASCS. Even if the farmer opted
to participate in the IYC program. the attractiveness of crop insurance
would not change drastically. Suppose this above average farmer
submitted three years of data showing he averaged 125 bushels/acre over
the period. This is averaged with seven years of county data (100
bushels/acre) to determine the insurable level. In this case his

adjusted average yield is 107.5 bushels/acre which means the maximum

insurable yield is 80.625 bushels/acre. Therefore. even with the IYC

93

26

program our farmer would have to suffer a decline of over 35 percent to

be eligible for a benefit from FCIC. These calculations are shown
below.
(1) Adjusted average yield = [(125 X 3) + (100 X 7)]/10

107.5 bushels/acre

(2) Maximum insurable yield = 107.5 X .75
= 80.625 bushels/acre
(3) Percent fall for benefit = (125 - 80.625)/125

= 35.5 percent

If this farmer has a three year crop rotation. meaning he
grows corn every third year on the farm in question. twenty-one years
will pass before he will be able to provide seven years of yield data
from his farm. If there is any sort of trend in yields. the ten years
of data from his farm will not give a very accurate picture of his
current ability to produce corn.

A second problem is that use of county data cannot capture
differences in the variability of yields on two farms. Suppose two
farmers. Jones and Smith. have the same expected yield but the
variability of Smith's yields is much greater. Figure 2.1 compares the
probability density function (PDF) of yields for Jones and Smith.
Suppose both select a policy from FCIC which guarantees them 75 percent
of their average yield. a much greater proportion of Smith's PDF is

covered than Jones' (The area a is much larger than the area aJ). If

S

Jones and Smith are signing up for insurance for the first time and

have land of similar quality. they will pay similar premiums. The

27

program will be much more generous to Mr. Smith since he will receive
indemnities more frequently and the size of his indemnities will. on
average. be larger. Normally the premium paid by Smith would be
expected to be much higher. reflecting his more variable experiences.
FCIC premiums do. in fact. adjust over time to reflect such differences
but only slowly. There seems to be no explicit inclusion of the
proportion of the PDF covered in the premium calculation formula.
Having developed this background in crap insurance. the

discussion now turns to the specific elements of a revenue insurance

program.

Probability

L, Yields

0.75u

 

 

I
I
I
I
I
I
6
|
I
1
U

Figure 2.1: Comparison of Smith's and Jones' PDF.

28
The Prospective Revenue Insurance Program

The idea of revenue insurance for farmers is not new. In
the late 19503 and early 19603 it was discussed in the academic

18 At that time revenue protection for farmers was proposed

journals.
as part of a comprehensive social insurance program and would have
compensated farmers in a manner comparable to workmen's compensation.
The current discussion of revenue insurance takes a somewhat different
tone. The 1981 Farm 8111 called for the creation of a task force to
determine. "whether such a concept (as revenue insurance) might provide
the basis for an acceptable alternative to the commodity price support.
income maintenance and disaster assistance programs currently

.19 The task force

administered by the Department of Agriculture
was duly formed and presented its recommendations to the United States
Congress in June of 1983. The recommendations of the task force will

provide a starting place for this description of a revenue insurance

program.

The Task Force Recommendations

The task force listed fifteen characteristics they felt a
revenue insurance program should possess. Table 2.1 summarizes these
characteristics.

Most of the ideas contained in the table are hard to fault.
The same cannot be said of the means they proposed to implement their
ideas. The outlines of the revenue insurance program envisaged by the
task force are as follows. First. they would offer coverage on a crop

by crop basis. Thus. a farmer could insure 75 percent of his average

29

Table 2.1: Characteristics of an Ideal Revenue Insurance Program

H

A

@4050!

‘D

10.

11.

12.
13.

14.

15.

‘AgiProppsedAby the Revenue Insurancengsk Force.

It should be actuarially sound.

It should be based on the yields of individual farmers and
prices in a well defined market area.

It should offer coverage on all crops or agricultural
products currently covered by a government program.
Additional types of output should be covered as practical.

It should be designed to attract a large number of eligible
farmers.

The program should be easily understood and administered.

. Moral hazard and adverse selection should be minimized.

Imprudent risk taking should not be encouraged.
Government expenditures and involvement in the agricultural
sector should be minimized.

. No more than 100 percent of cash costs of production should be

covered.

Coverage in an area should be offered only on products proven
to be commercially viable.

Disruption of related markets caused by the program should be
minimized.

Price signals should not be distorted.

It should complement and not substitute for existing
insurance options.

It should be flexible enough to accommodate changes in
productivity and production practices.

Sound management practices should be followed and isolation
from the political arena sought.

revenue from his corn crop and. if he wanted to. 50 percent of his

average revenue from soybeans. Second. coverage would be offered for

multiple year periods. For example. if farmer Jones wanted to guarantee

a revenue level from his corn crop he would have to buy a policy

covering the next three cropping seasons. Third, the Task Force

recommended use of farm data for yields but an average market price

from "a well-defined market area". to determine the revenue earned by a

participating farmer in a given year. Fourth. premiums charged for

this protection would be sufficiently high to cover indemnities and

administrative costs. Fifth. the guaranteed return would not exceed

this farmer's cash costs of production. Sixth. the program would be run

30

entirely by private insurance companies. Private insurers were felt to
be more efficient managers of insurance programs. It was also argued
that private insurers are held in higher esteem than government

bureaucrats by the farm population.

An Alternative Program Formulation

The program analyzed in this dissertation differs from the
Task Force program in several significant ways. Table 2.2 summarizes
my assumptions about the form a revenue insurance program should take.
Coverage should be based on gross farm receipts from all farming
activities, not on a crop by crop basis. Production costs and off-farm
income would not be considered in calculating protection levels.
Coverage would be offered at various proportions of the average real
gross receipts earned from each crop cycle over the past ten years.
The levels of 50 percent. 60 percent and 75 percent were used in this
study. Gross receipts would be calculated as sales of the current
year's output plus or minus changes in the value of inventories held.
Inventories would be appraised at year's end using six—month contracts
on the futures market, if available. or the current market price for
the commodity if a futures market for it does not exist. Premiums paid
by farmers would be calculated on the basis of the frequency and size
of benefits received and would, at a minimum. cover indemnities.
Policies would be marketed and serviced by private insurers and

reinsured by the federal government.

31

Table 2.2: Summary of the Alternntive Revenge Insurnnge Prognam

. Coverage for gross revenue from nll_farming activities.

. Coverage offered at 50. 60 and 75 percent of average gross
revenue.

Base period for estimating coverage is 10 years.

. Premiums based on frequency and size of payouts.

Premiums at least cover indemnities.

Inventory changes evaluated at year's end using agreed upon
formula.

Coverage and premiums calculated from farm data.

Coverage should be adjusted to account for inflation.

. Policies sold by private insurance companies.

Policies reinsured with the federal government.

@0050) NH

O‘DQQ

Justification for Alternative Formulation

This discussion must start with a justification for insuring
gross farm receipts rather than gross receipts from a single crop.
There are at least three reasons for this approach. First. gross farm
receipts is a variable much closer to the one of primary concern to
most farmers, net profits. than is gross receipts from a single crop.
Therefore. a program guaranteeing a given level of gross receipts is
more likely to be of interest to a broader cross section of farmers
than one guaranteeing gross receipts from a single crop. Second.
insuring returns from a single crop could easily promote behavior I
would consider counterproductive. Two hypothetical situations should
suffice to illustrate this point. Consider a farmer faced with a
situation in which two of his crops require immediate attention because
of an infestation of pests. If one crop is insured and the other is
not, which crop will receive the needed attention? In case two a
farmer is considering revenue insurance for one of the two crops he
PPOduces. Based on past experience. he knows that crop "a" produces
Very little revenue once every3 or 4 years while crop "b" has a

Sillilar experience once every 20 years. Our farmer is much more likely

32

to purchase insurance on crop "a". This could mean that the insurance
pool is filled with bad risks. in which case the premiums required to

cover indemnities would skyrocket and the program fail.

The third justification I would offer for using gross farm
receipts is that this would allow the insurer to take advantage of the
revenue experiences of different types of output that are unlikely to
be perfectly positively correlated. For instance. if a farm produces
corn and soybeans. a bad revenue year for corn may be wholly or
partially offset by a better than average year for soybeans. This will
reduce the cost of a revenue insurance policy. The implication of this
formulation is that risks are spread across types of crops and across
time. This feature should facilitate the pooling of the hazards faced
by the farm population.

The justification for seeking a premium that. at a minimum.
covers indemnities rather than one covering all costs is two-fold.
First. in the early years of the program it will be important to
maximize participation levels to increase the probability that premiums
do cover indemnities. As a new policy direction. revenue insurance is
bound to face considerable hostility from farmers and from those with
vested interests in the current programs. Acceptable participation
rates are more probable if the price of insurance is kept down. Good
participation is also necessary to maintain the political will to
continue the program. If the program experiences large losses
initially and few farmers participate. revenue insurance could suffer
the same fate crop insurance did in its early years (cancellation.
l‘eduction in scope. etc.). An insurance program requires continuity to

{Utlction properly. Insurance works because the seller can use the long

33

term probabilities facing his clients to cover a portion of their
risks. In addition. continuity promotes farmer confidence in the
program.

The government should be involved because it is unclear that
a private company could or would offer this form of insurance on its
own. As noted at the start of this chapter, it is difficult to
envisage a private insurer offering revenue insurance. Currently we
lack the data and the understanding of the complex interaction of
forces that determine a farmer's revenue.

Some have suggested that insurance companies might offer
this type of coverage if option markets were available to allow
insurance companies to shift some of the risk they would be assuming by
writing a revenue insurance policy. This is not likely to be true even
if revenue insurance is offered on a crop by crop basis (and is less
likely if it is offered on a whole-farm revenue basis). An options
market would allow an insurance company to protect itself against
intra-year but not inter-year price movements. There is a very basic
conflict between the types of protection offered by revenue insurance
and an options market. An options market allows a participant to put a
floor (if a seller) or a ceiling (if a buyer) price on the commodity
with which he is dealing. The protection is against price movements in
the near future. In essence. an options market is designed to shift
risk bearing responsibilities caused by exogenous events which affect
market prices within a given cropping season. Clearly. longer term
options could be written but as the length of time covered by the
options contract increases. the cost of purchasing the option would be

expected to increase dramatically.

34

A revenue insurance policy. in contrast. is offering
protection from major deviations from longer term trends. In addition,
the program discussed in this thesis is based on coverage for total
farm earnings. Since many farmers produce more than one type of crop.
option contracts would have to be taken out on each of the crops
produced to offer the insurer comprehensive protection. Obviously the
transactions costs increase substantially in this case.

An additional reason for governmental involvement is the
danger that a relatively wide-spread phenomena. such as last year's
drought in the mid-West. could threaten the economic viability of a
private insurer who had issued many policies in the affected region.
Finally. the government is almost certain to be involved in the data
collection efforts needed for the successful operation of the program.

Cost of coverage should be based on farm data so that
premiums charged reflect the individual management decisions of the
client. This is not likely to be possible in the extreme: the premium
for each farmer will not be calculated using a unique formula. It is
conceivable that different classes of farmers will have their premium
calculated differently.

The level of coverage should also be adjusted to account for
inflation. This is particularly important if a relatively long base
period is used since the dollars earned in the early years of the base
period will be relatively more valuable than those earned in the
current period.

Allowing private insurers to market and service revenue
insurance contracts while offering a governmental reinsurance option

has several advantages. First. since an insurance agent has an on-

35

going relationship with a farmer and is accustomed to explaining
insurance contracts. they may be effective conduits of information
about the new program. Second. since revenue insurance would be
expected to supplant other forms of agricultural insurance. giving
private insurers an economic stake in revenue insurance might defuse
the expected opposition of the insurance companies to the program.

Finally. the adminstrative details of the program. such as
the length of the base period and the coverage levels offered should be
open for debate. They are. to a large extent, empirical questions.
The base period, for example. should be sufficiently long to provide an
accurate picture of the farmer's earning potential. If it is too long.
however, its ability to adust to changing conditions is reduced. The
level of coverage offered should be neither so high as to "guarantee"
success nor so low as to fail to offer a meaningful level of
protection. The levels chosen for this analysis should be seen as a
starting point for discussion.

Having summarized and justified the assumptions employed
about the structure of a revenue insurance program. I will proceed with

a discussion of the theory of insurance.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

36

. Countries who have or have had crop insurance programs of some sort

include: Canada. Chile. France. Greece. Israel. Japan, Mauritius.
Mexico, Poland. Spain. Sri Lanka. Sweden. the U.S.A. and the U.S.S.R.

. Canada. Report of the Federal Task Force on Agriculture. "Canadian

Agriculture in the Seventies". Page 390.

. P. X. Ray. 1981. Page 194.

. Ray, ibid. Page 198.

. Ray. ibid. Page 200.

. Ray, ibid. Page 202.

. Ray. ibid. Page 204.

. Roger Henri Millot. 1969, Page 278.

. Beatriz Benilde Galan. 1981. Page 14

Millot. op. cit.. Page 121
Millot. op. cit.. Page 128-129
Millot. op. cit.. Page 177
Millot. op. cit.. Page 179

Krammer. 1982 and Gardner and Krammer. 1982. two recently
published summaries of this experience. are quite good.

United States, U.S.D.A., An Inside Look at Crop Insurance". March
1980.

Vernon L. Sorenson. March 1982. Page 1.
Walker. Odell. 1982. Page 1.
See Swerling. 1959. for an example of this discussion.

United States. U.S.D.A.. "Farm Income Protection Insurance: .A
Report to the U.S. Congress". June. 1983. Page 33.

Chapter 3

A Summary of Empirical and Theoretical Studies of Insurance:
The Economic and Psychological Schools

The extensive literature on the behavior of individuals
choosing insurance may be divided into two schools of thought. One
school is psychological in nature. the other is economic.
Psychologists attempt to determine people's behavior in risky
situations by asking them about their preferences or observing their
actions in such situations. Economists prefer an axiomatic approach:

inferring actions from assumptions about behavior.1

This chapter will
review a subset of the models employed and conclusions reached by

authors from both schools of thought.

The Economic Approach

The economics literature in economics dealing with insurance
can be divided into four parts: theoretical models of insurance
demand. theoretical treatment of insurance supply. empirical
investigations of insurance demand and empirical work on insurance

supply.

Theoretical Models of Insurance Purchases
Of the demand models reviewed here. most introduce
uncertainty by considering an ex-ante decision when two outcomes are

possible. Outcomes are dependent upon the state of nature that

37

38

prevails after the decision is made. The outcome associated with one
state of nature will be less favorable than the outcome associated with
the other. A few studies refine this slightly by introducing a
stochastic loss function producing outcomes of varying degrees of
utility.

As an example of these two state models. suppose you are a
farmer in the kingdom of Oz. The climate in Oz is such that twenty-
five percent of the time a frost occurs during the night of April 20th.
Otherwise. frosts do not occur in Oz. As an Ozian farmer. you know
that if there is no frost. planting corn on April lst will result in

yields ten percent greater than those attained if you wait until April

20th to plant. If a frost does occur. replanting is necessary and
costs increase by seventy—five percent. The ex-ante decision on April
lst is how many acres. ' if any. should be planted. The

favorable/unfavorable state is no frost/frost.

Ahsan. Ali and Kurian develop a two state model with risk
averse buyers of insurance and risk neutral sellers. Assuming a zero
profit level for insurers. they maximize the following expression:

Maximize V - (l-p)U(Yl) + p(U(Y2;) (3.1)

Subject to W = a(qA - pF(A)) = 0 (3.2)

Where

= Buyer's expected utility.

Buyer's utility function.

a Seller's profit function.

2 Probability of an unfavorable event.
Income earned in state i. i = 1.2.

= Farm's output or production function.
Resources devoted to risky production.
Premium rate.

Profits.

Insurance coverage ratio.

>~<
t=<
u u

mtn>vuo

Fl

39

Equation (3.1) states that the utility of the farmer is the
sum of the utility associated with the favorable outcome times the
probability that the favorable state occurs and the utility of the
unfavorable state times the probability it occurs. The authors solved
this model to determine optimal insurance choices and found that risk

3

averse farmers will purchase full insurance if it is offered at an

actuarially fair price4. With full insurance more resources go into
the risky asset than when full insurance is not available. If returns
to the risky asset experience a mean preserving spread. allocation of
resources to the risky action choice will decline. A mean preserving
spread is a change in the PDF which leaves the mean unchanged while
increasing the variance. As initial wealth or the minimum level of
insured income increase or as the risky action choice experiences a
risk-preserving increase in the mean, more resources will go into the
risky option. A risk-preserving increase in the mean holds the shape

of the PDF unchanged while shifting the entire distribution outward.

Ehrlich and Becker also use a two—state model in their

examination of the relationships between market insurance. self
insurance and self protection. Their basic model is similar to
equations (3.1) and (3.2). However. the definition of income in the

two states and the constraint change, depending upon the risk reducing
options available to the decision maker. Thus, if only market
insurance is available. the income expression and budget constraint are
different than if self protection is the only risk reducing option. In
all cases, the models are solved to determine the implications of and
relationships between the various forms of protection. The authors

first look at the characteristics of market insurance. They also

4O

conclude that full insurance will be purchased if available at an
actuarially fair price.

In examining the impact of an increase in the premium.
Ehrlich and Becker suggest that the premium be thought of as the rate
at which a consumer is willing to trade income in the favorable state

for more income in the unfavorable state.5

Viewing the price of
insurance in this way allows them to analyze the purchase decision
using standard consumption theory. In Figure 3.1 the impact of an
increase in the price of insurance is presented graphically. The
initial equilibrium is at point a, the point of tangency between the
iso-utility curve U1 and the income transfer line DE. With an increase
in the premium. the cost of maintaining income in the unfavorable
state, Y1, increases, and the transfer line becomes DF. To arrive at
the new equilibrium, point c. income and substitution effects can be
identified. The substitution effect moves the consumer from point a to
point b. the point of tangency between the iso-utility curve and the
income compensated budget line. IH. The income effect moves him to
point c. The substitution and income effects are both negative when

income in the unfavorable state becomes relatively more expensive to

maintain. As a result, demand for income in state 1 decreases and less

insurance is purchased. The impact of an increase in the premium on
demand for Y2. income in the favorable state. is ambiguous. As the
authors point out, "although an increase in . . . (the premium)

reduces the amount of insurance purchased. each unit purchased becomes

6 Therefore. the impact on income realized in the

more expensive."
favorable state and on the amount spent on insurance will depend upon

the elasticity of demand for insurance.

41

 

Y
F I E 1

Figure 3.1: Income and Substitution Effects for Insurance Purchases

Erhlich and Becker also examine the impact of a change in
the initial wealth position of the decision maker on demand for
insurance. They derive the interesting conclusion that the effect of
an increase in wealth depends upon how the increase is distributed
between the two states of nature. If wealth in both states increases
by the same percentage and the slopes of the indifference curves are
constant along a ray from the origin (implying constant relative risk
aversion). no change in the amount of insurance demanded will be
observed. If wealth only increases in the favorable (unfavorable)
state. demand for insurance will increase (decrease).

If market insurance is not available. a decision maker will
engage in self insurance if it increases the income he will realize in
the unfavorable state and if the price is less than the probability
weighted ratio of the marginal utility of income in the bad state to

the marginal utility of income in the good state. Self insurance will

42

increase as the marginal productivity of such expenditures increase or
as the endowed level of income in the unfavorable state falls. Ehrlich
and Becker conclude there is little incentive to self insure against
low probability events because the price of self insurance is
"independent of the probability of loss."7

Changes in model parameters affect demand for market and
self insurance differently if both options are available. Thus. if
demand for market insurance increases in response to a decrease in
income in the unfavorable state. demand for the substitute. self
insurance. will fall. Ehrlich and Becker also conclude that a decrease
in the probability of the unfavorable event will decrease the demand
for self insurance and increase demand for market insurance. This
result derives from their assumption that the price of market
insurance. unlike the price of self insurance. is related to the
probability attached to the unfavorable state of nature. They conclude
that people will use market insurance to protect themselves against low
probability events. Finally, if market insurance is available at an
actuarially fair price. and self insurance is also available. they
predict that behavior resembling risk neutrality should be observed.
Decision makers. in this case. choose action choices that maximize
expected income. The authors conclude that "apparent attitudes toward

risk are dependent upon market opportunities, and real attitudes cannot

easily be inferred from behavior."8 Robison and Lev (1984) makes a
similar point.

Finally. the relationship between self protection and
insurance is explored. Ehrlich and Becker indicate that insurance has

two opposing effects on self protection. To the extent that insurance

43

reduces the difference between favorable and unfavorable outcomes. the
incentive to engage in self protective actions is diminished. However.
if the, price of insurance is inversely related to the level of self
protection. there is an incentive to increase expenditures on self
protection. Thus. self protection can be either a substitute for or a
complement of insurance.

To gain insights into intertemporal choices involved in
purchasing insurance. Viscusi developed a two state. comparative
statics model in which decision makers maximize their subjective
- utilities over two periods. In his model. insurance premiums are
exogenously determined. The two states are accident and no accident
and the insurer can monitor only the outcome. not the extent of self
protection practiced. Table 3.1 summarizes Viscusi's results.

Viscusi found that to the extent a buyer can determine the
likelihood of having an accident. his average income will rise because
he will reduce expenditures on self protection and will selectively
purchase insurance. For similar reasons. Viscusi found that as the
mean of the accident likelihood distribution becomes larger and the
variance smaller. the insurance buyer will purchase more insurance and
practice less self protection. The impact of these changes on average
income will be ambiguous. Table 3.1 tells us that as the future-
mindedness of individuals, as represented by a fall in the discount
factor. increases. so will their purchases of self protection. An
increased concern for the future means the buyer will be sensitive to
potential increases in his insurance premiums. To reduce the
likelihood of increased premiums. expenditures on self protection are

increased. An increase in the discount factor has a negative impact

44

on average income and purchases of market insurance. Particular
attention should be drawn to the pattern of responses with respect to
insurance and self protection. Table 3.1 indicates "all unambiguous
effects of parameter changes have opposite impacts on (the level of)

self protection and insurance (purchased)."9

The implication is that
any manipulation of parameters can increase either the extent of self
protection or the amount. of insurance purchased but not both
simultaneously. This result seems to contradict Ehrlich and Becker who
concluded that self protection and insurance could be substitutes or
complements. The results are actually consistent. Viscusi assumes the
price of insurance goes down as expenditures on self protection go up.

Ehrlich and Becker allow for independence between these factors but

show that if they are negatively related they will be substitutes.

 

Table 3.1: Summary of Viscusi's Comparative Statics Results10
Increase in Effect Effect Effect on Effect on
Exogenous on Y1(a) on Y2(b) Self Pro- Market In-
Variable tection surance

Expenditures Expenditures

 

 

Sharpness of Prior
Assessment of + 0 - +
Accident Likelihood
Beta Distribution
Factor(c) + - - +

Discount Factor(d) - 0 + —
Price of Insurance.

Period 1 ?(e) ? ? ?
Price of Insurance.

Period 2. no + 0 — +

Accident in 1

Price of Insurance.
Period 2 - 0 + -
Accident in 1

 

 

(a) Y1 is income in period 1.

(b) Y2 is income in period 2.

(c) Beta—distribution factor defines the mean and
variance of the probability of an accident.

(d) = 1/(1+r) where r is the interest rate.

(e) ? = ambiguous effect.

45

The final three lines of Table 3.1 illustrate the importance of
merit pricing. Viscusi argues that the price of insurance in the first
period will have an ambiguous impact on both insurance purchases and
self protection efforts because this price is independent of individual
action. Indeed. the main impact of raising the price in the first
period is to discourage low risk people from purchasing insurance
resulting in a problem with adverse selection.11 What is of more
importance in Viscusi's model is what happens in the second period. If
merit pricing is not practiced. where merit pricing implies that
premiums are raised or lowered in accordance with the accident record.

d12 are

then the problems of adverse selection and moral hazar
magnified. This agrees with results obtained by Ehrlich and Becker.

A very different approach to analyzing insurance purchase
decisions has recently been proposed by Heiner. Heiner's thesis is
that human behavior can be understood and predicted "only to the extent
that uncertainty prevents agents from successfully maximizing."13
Central to his argument is what he terms the 'Competence-Difficulty' or
0-0 Gap. The C-D Gap is the difference between the competence of the
decision maker and the difficulty of choosing the alternative which
would maximize his utility. While most economic analysis assumes the
C-D Gap is zero, Heiner argues this is rarely the case and a positive
C-D Gap causes 'flexibility constrained behavior'. Both environmental
variables. such as the complexity of the situation. the stability of
relationships and the likelihood of occurrence. and perceptual
variables. such as differing abilities to decipher relationships.

contribute to the C—D Gap. Heiner develops a 'reliability condition'

which sorts situations into groups calling for flexible or inflexible

46

responses on the part of the decision maker. The mathematical

expression for this reliability condition is:

MUJ/th) [‘1(eugaeilhi-1laej1'l/‘1l'teJl (3-3)
or
"(U)¢9(9)(“(23?3 3 w(U)(lfekfii - Kiel»! (3.4)
Where:
r(U) = Conditional probability of choosing a new action choice at

the appropriate time.

w(U) = Conditional probability of choosing a new action choice at
an inappropriate time.
1(e) a Loss in performance associated with w(U).

g(e) = Gain in performance associated with r(U).
1(9) = Probability that the right time to select a new action
choice occurs.

The ratio on the left side of the inequality in (3.3) is referred to as
the reliability ratio and the one on the right is called the tolerance
limit. The reliability ratio measures the decision maker's ability to
make the correct decision at the correct time. The tolerance limit
measures the expected cost that must be incurred (for a given
reliability ratio) to induce action on the part of the decision maker.
When the strict inequality in equation (3.3) does not hold, a decision
maker should not invest time and money exploring the available options;
current standard operating procedures should be maintained.

Heiner draws four behavioral generalizations from the
reliability condition. First. action choices which would be preferred
in rarely occurring situations are excluded from a decision maker's
choice set. Second, over time the set of action choices available will
"tend to produce rules that systematically restrict the flexibility of

14

behavior" and will not approach optimizing behavior. This concept

47

might be compared to the systems science tenet that the optimal
performance of the system as a whole is rarely achieved by maximizing
in a single time period or over a specific subcomponent of the larger
system. Third. behavioral patterns that are counterproductive may
persist even though the cost of this behavior may be high. In terms
of equation (3.3). a rule for behavior may persist despite a large r(U)
if is small. In the operant conditioning terms of Skinner, aberrant

behavior can persist even in the face of powerful disincentives if a

negative reinforcer is not received. Finally. Heiner argues that the
greater the degree of uncertainty the more predictable behavior. In
equation (3.3), an increase in uncertainty decreases r(U) while

increasing w(U).

With respect to the insurance purchase decision, Heiner's
model indicates that people will be unlikely to insure against events
with a low probability of occurrence. Heiner argues this is the
explanation for the observed reluctance of home owners on flood plains
to purchase federal flood insurance at lower than actuarially fair
rates. As Heiner puts it, "as the probability . . . of a disaster goes
to zero, the number of such extremely rare but conceivable events grows
indefinitely large. Given any positive set-up costs of insuring
against each of these possibilities. the total insurance cost will

15 As (e) gets small.

eventually exceed a persons's (finite) wealth."
the tolerance limit gets quite large and the reliability ratio must be
very large if insurance is to be purchased to cover the hazard. But.
at the same time. rare events are likely to reduce the decision maker's

reliability ratio.

Heiner's results run counter to those of Ehrlich and Becker

48

in at least one respect. Ehrlich and Becker argued that insurance
demand will increase as the difference between good and bad outcomes
increases. Heiner makes the quite reasonable point that it is not
simply the dollar difference between the two but the probability
weighted difference. Thus. the difference between good and bad states
could increase yet, if the probability of the bad state occurring drops
to near zero, the demand for insurance could decrease. Heiner does not
examine the relationship between market insurance and other mechanisms

for protection.

Empirical Models of Insurance Purchases

In examining the U.S. experience with crop insurance,
Gardner and Krammer conclude that the program has suffered from adverse
selection. has substituted for diversification and is used more heavily
by part owners (whom they hypothesize are more highly leveraged) than
by tenants or full owners. Using regression analysis. they found the
expected rate of return to be significant and positively correlated
with participation rates. They also found evidence to support the
hypothesis that recent experience with crop insurance was more

important in the purchase decision than longer term experience with the

program.

Like Gardner and Krammer. Walker found that farmers view
crop insurance as an investment. Hence, he would expect greater
participation if the return on investment increased. Walker also

concluded that the relationship between a farm's cash flow position and
insurance purchases could be positive or negative. If lenders forced
farmers facing cash flow problems to purchase insurance as a

prerequisite for a loan. the relationship would be positive.

49

Otherwise. he expected a negative relationship.

King and Gamek estimated that purchasing the highest level
of protection from FCIC (75 percent of yield and the highest price
election). would increase the variable costs of dryland wheat farmers

in Colorado by 30 percent.16

They hypothesized that such a heavy
burden decreases participation. In another paper also dealing with
dryland wheat farmers in Colorado. King reported the results of a
simulation model that used stochastic dominance with respect to a
function and interval risk preference measures to order insurance
choices and to examine the impact of changes in model parameters. His
model was reasonably successful in predicting the actual choices of
farmers. He found that changing the price of insurance by plus or
minus ten percent had little impact on participation. Basing premiums
on actual farm experience increased farmer participation in the
insurance program.

Finally. Attansi and Karlinger examined the impact of the
absolute risk coefficient on demand for flood insurance. The authors
found that an increase in this coefficient was associated with a shift
out in the demand for flood insurance and a decrease in price
elasticity. Furthermore. they found the absolute risk coefficient to

be positive (implying risk aversion) and fairly constant across the

towns in their survey.

50

Theoretical Models of Insurance Sales

Raviv. using the following model, examines the optimal form

for an insurance policy :

Maximize B(U(W + I(x) - p - x)) > E(U(W - x)) (3.5)
Subject to E(V(Wo + p - I(x) — C(I(x)) > V(Wo) (3.6)
Where:
U(W) = Utility function of a consumer. U' > 0. U" < 0
V(W) - Utility function of an insurer. V' > 0. V” < 0
W0 = Initial wealth of insurer
W . Wealth of consumer
I(x) = Indemnity schedule with 0<I(x)<x and 1(0) = 0
p = Premium
x a Loss
C(I(x)) 8 Cost of providing insurance. C(O) = a > 0.

C' F 0 and C" F 0.

The left side of the inequality in equation (3.5) is the
expected utility of the buyer if an insurance policy is purchased and
the expression on the right is utility if no policy is purchased. The
expression on the left side of equation (3.6) is the expected utility
of the seller if an insurance policy is sold and the one on the right
is utility if a policy is not sold. Both inequalities have to hold if
the solution of this system is non—empty. Raviv concludes that an
optimal policy will have a deductible if the cost of providing
insurance is a function of the type of coverage offered or if the
seller is risk averse. If the insurer is not risk neutral or if C" is
strictly greater than zero. the optimal policy will have both a
deductible and coinsurance.l7

In the Ahsan. Ali and Kurian model discussed earlier. the

conclusion is reached that if there are different risk classes of

51

farmers. an equilibrium in the insurance market will not be attained
unless the insurer can distinguish between the different classes
perfectly. A corollary to this result is that informational
externalities are sufficient to explain the lack of insurance markets
in agriculture noted in Chapter 1.

Rothschild and Stiglitz use a graphical analysis to show why
an equilibrium might not exist in an insurance market of non-
homogeneous buyers. Their basic argument can be illustrated using
Figures 3.2 and 3.3. In Figure 3.2. the lines ED and BF represent
contract lines. rates at which Y1 and Y2 are traded. for high and low
risk insurees respectively. that yield zero profit for the seller. The
buyers' preferred paints are Ah for the high and B for the low risk

group. Both points offer the respective consumer full insurance.

Full Insurance Line

 

45° v

Figure 3.2: Insurance Offerings to Low and High Risk Buyers

Unfortunately. B is not a viable policy unless the seller

can discriminate perfectly between the two groups. B is preferred by

52

all high risk buyers. as it would move them to a higher iso—utility
curve. and by the low risk group. However. if high risk buyers
purchase a contract at B. the insurance company would earn negative
profits and would soon be out of business. An insurance policy that
would not attract high risk consumers yet leave low risk customers as
W811 Off as possible is Al since this point is on the same iso-utility
line and would therefore not induce high risk consumers to move away
from Ah which offers them full insurance. However. even the
combination (Al'Ah) may not be an equilibrium. Consider the point c.
Both high and low risk customers would prefer c to Ab and Al since
both would move to higher iso-utility curves. The point 0 might also
satisfy the zero profit requirement. depending upon the relative
numbers of low and high risk individuals covered by the insurance
company.

Rothschild and Stiglitz show that c is not a viable
equilibrium point. In Figure 3.3. we assume point c is on the zero
profit line. If a different insurance company offers a contract such
as m. all low risk consumers will prefer m to c. However. at m the
insurer earns a profit because m is below the rate at which low risk
buyers must trade Y2 for Y1 in an actuarially fair system (the line HP
in Figure 3.2). This means the insurer would take in more in favorable
states than he disburses in unfavorable ones. Because a profit is
earned. the combination (c.m) cannot be an equilibrium. Another firm
will offer a plan similar to m but at a lower profit rate. This will
continue until the zero profit line is regained. Rothschild and
Stiglitz conclude that the only possible equilibrium in a market with

CW0 CYDGS of buyers is (Al'Ah) and that even this equilibrium may not

53

exist. This implies that a pooled contract is impossible and separate
contracts may not provide an equilibrium either. Specifically, they
conclude that if there are only a few high risk consumers or if the
cost of separating consumers is high. an equilibrium will not be

attained.

Y Full Insurance Line
2

 

.50
Y1

Figure 3.3: Disequilibrium in an Insurance Market with Two Groups of
Buyers

Another interesting insight provided by Rothschild and
Stiglitz is that the presence of high risk individuals creates a one
way externality. The low risk group cannot achieve full insurance yet
this does not benefit the high risk group by reducing their premiums or
extending their coverage.

Spence and Zeckhauser examine the relationship between full
insurance and moral hazard by considering the information an insurance
seller can monitor. Their basic model assumes a consumer maximizes the
expected value of a von Neumann — Morgenstern utility function subject

18

to a break-even constraint for the seller. The arguments of the

utility function and the constraint vary. depending upon the

54

information available to each group. The key components of their model
are the sequencing of moves between individuals and the state of
nature. and the information state monitored by the insurer. Sequencing
refers to when the individual has to choose his desired level of
coverage; before or after the state of nature is determined. The
information state refers to what the insurer can monitor. The
possibilities are the state of nature or the insuree's actions. his
expenditures on self protection for instance. The authors conclude
that if the insurer can monitor the state of nature directly or
individual actions in advance of the state of nature (and alter the
insurance pay-off schedule to induce the individual to act in a manner
it deems optimal). then full insurance can be provided without causing
problems of inappropriate incentives. However. if the insurer can
monitor individual actions only after the state of nature is realized.
or the effect of the state of nature on the buyer's insured variable.
neither complete risk spreading nor appropriate individual incentives
will be possible. Again an information cost causes less than optimal
performance in the insurance market.

Hogan argues that a way to avoid moral hazard in crop
insurance is to make it compulsory. Compulsory crop insurance has the
additional advantage that it would allow financial risk to be more
equitably distributed by lending institutions. Hogan states that
currently. every creditor poses a threat to the economic viability of a
bank in that he/she may default on a loan. As a result. every borrower
is charged a flat fee. in the form of a higher interest rate. to cover
the expenses caused by those who do default. Since each creditor does

not pose the same degree of risk, what is needed is a way to allocate

55

the cost of bad debts to those who pose the greatest threat. Compulsory
crop insurance is. according to Hogan. such a mechanism. Hogan's
assumption is that the price of crop insurance would vary by farmer
according to the riskiness of the farm. The insurance contract would
be offered as collateral for the loan and the premium paid by the
farmer would allocate the financial risk according to the exposure to
hazard.

The model developed by Viscusi. summarized in Table 3.1.
addresses income and portfolio effects faced by an insurance seller
practicing merit pricing. Merit pricing refers to the practice of
linking the price of insurance to outcomes in the previous period.
Viscusi concluded that because of the inverse relationship between
insurance purchases and self protection. merit pricing will have
important implications for a seller. Consider a buyer who doesn't have
an accident in the first period. If. as a result of his good record.
his insurance premium falls in the second period. Viscusi's model
predicts he will respond by investing in more self protection and less
insurance. The result. for the insurance company is two-fold. First.
larger expenditures on self protection would be expected to reduce the
amount of benefits the insurance company would have to pay to this
buyer. On the other hand. less insurance is purchased by this now-
safer consumer which reduces both the importance of this buyer in the
company's risk portfolio and the seller's revenue. The net effect on

the seller's income is. therefore. ambiguous.

Empirical Models of Insurance Sellers

Explicit empirical models of insurance sellers are few.

56

However. King's work. cited above, provides useful insights into
variables that might be important to insurance sellers. First. King's
work indicates that use of a farmer's subjective beliefs about his
yield distribution is the best predictor of farmer actions. He derives
these yield distributions by means of a series of questions included in
a computer simulation. This information could be used to determine
premiums and would provide a better loss ratio for the insurer. In his
work King estimated minimum and maximum expected loss ratios under a
variety of assumptions about program parameters. He found that when
using the subjective yield distribution. the minimum loss ratio rose
while the maximum fell. relative to the case in which premiums were
based on county averages. The reduced maximum expected loss ratio was
attributed to reduced problems with adverse selection.

King also suggests the use of the entire historical yield
distribution rather than just the mean to determine the terms of the
insurance contract. Specifically. inclusion of a measure of the
probability of paying an indemnity to a given farmer would improve the
performance of the system. This is. in essence empirical confirmation
of the phenomenon illustrated in Figure 2.1 on page 27. where the PDFs
of Jones and Smith were compared. King's research indicates that
greater use of the information contained in a farmer's PDF would
increase participation. improve program performance and increase the

equity of coverage offered.

57

THE PSYCHOLOGICAL APPROACH

The analysis of risk and insurance purchase decisions by
psychologists tends to be more empirically oriented than the approach
favored by economists. Psychologists have been concerned almost
exclusively with the behavior of buyers of insurance. not sellers.
Based on their empirical work. psychologists have rejected many of the
von Neumann - Morgenstern axioms which underlie most economic theories
about the behavior of economic agents in risky situations.

In the mid-19503. Allais identified a condition that has
come to be known as the Allais paradox or the certainty effect.
Generally. what this says is that decreasing the probability of two
events by the same proportion will have a larger impact on the utility
associated with what had been a certain event than on an event that was
merely highly probable. Tversky and Kahneman present the following
example of the Allais paradox. Seventy-seven people were given the
following choice:

1. A sure win of $30 or
2. An 80% chance of winning $45.

Seventy-eight percent of the respondents chose the sure thing. In
contrast. fifty—eight percent chose to play for the $45 prize in the
following game:

3. A 25% chance to win $30 or
4. A 20% chance to win $45.

In the second game both options were reduced by the same
factor .four, vis—a—vis the first set of options.19 Based on the von
Neumann-Morgenstern assumptions. the expectation would be that someone
who prefers choice 1 to choice 2 in game one would prefer choice 3 to

choice 4 in the second game. The empirical results reported above

58

apparently contradict the axiom of consistency.

Maitel reporting on work done by Tversky offers an example
that seems to contradict the axiom of transitivity. Consider the case
of a man going to buy a car. Upon arriving at the showroom, he states
he wants the basic. no-frills model. He is quoted a price and told
that for a few dollars more he can have a model with a radio. For a
few dollars more than that. he can have power brakes: for a few dollars
above the third price he can get power steering; and so on. At each
stage he decides he will purchase the extra equipment. Finally. when
the car is loaded with additional equipment he is told that this new
car now costs twice what the basic version was going to cost him. At

20 At each

this point he decides to buy the stripped down version.
stage the buyer preferred the car with the additional piece of
equipment yet he preferred the no-frills car to the car with all the
extras. The story. while not an actual case. is plausible enough to
bring into question the universality of the transitivity property.
Katona believes that at any given time either good or bad
news is salient in a person's mind and good or bad news is thought to
have only good or bad effects. In addition. he feels that people adopt
rules of thumb when facing uncertain choices. Both cases imply that
people do not behave rationally in the sense used by economists.
Grether also questions the economists' approach to studying
behavior in risky situations. He points to some of the inconsistencies
noted above. people's frequent adoption of strategies that seem. to the
observer, to be non—optimal and to their substantial and systematic

biases in estimating the probabilities of events. He also cites a

great deal of evidence showing that people do not use information very

a:

59

efficiently. In particular. most decision makers do not use Bayes

Theorem to revise their probability beliefs.21

Tversky and Kahneman used the accumulated empirical
information to develop what they have termed "Prospect Theory". In

prospect theory the decision maker maximizes an expression of the

following general form:

Maximize si(pi)*v(xi)

Where
Pi = Probability of occurrence of event 1
V(Xl) = Value of outcome i.
81 = weight applied to probability pi.

Furthermore. they hypothesize that the shape of the value function is

as shown in Figure 3.4. The shape of V(x) implies that the displeasure

Utll 1:7

'(G‘l .......

p.....--.

I"
.—

Losm Ca in

 

O
"‘.

coca-uonoouq

   

------‘V(L“

 

Figure 3.4: The Value Function as Hypothesized by Prospect Theory

associated with a given loss. L1, is greater than the pleasure of

60

gaining a similar value, G1, [|V(L1)|>|V(Gl)|]. The shape of V(x) and
the choice of the (0.0) point. are critical factors in explaining
choices under risk. Setting the reference point. (0.0). determines
whether a given outcome is considered a gain or a loss. Given the
shape of V(x). a shift in the choice of the reference point. or
"frame". can alter the preference ordering of an individual.

To conform with empirical findings, Tversky and Kahneman
chose a functional form that overweights low probability events and
underweights high probability events. They restrict the form of s(p)
further by requiring low probability events be overweighted by a
smaller proportion than high probability events are underweighted.
Finally. they make both s(p) and V(x) non-linear functions. Non-
linearity of these functions helps to account for the framing phenomena
mentioned above (since the values associated with losses and gains can
change in different ways).

Robison (1982) raises questions about prospect theory. not
because of its lack of empirical validity. but because s(p) is loosely
defined. We do not know how to measure or estimate s(p) nor do we know

how it might change across people or time periods. Tversky and

Kahneman hold that the function "summarize(s) a common pattern of

choice"22.

Kunreuther and Slovik studied the patterns of home insurance
purchases in areas prone to flooding or earthquakes. They found
framing to be an important factor. For instance. many people in these

areas did not purchase insurance against the specific hazard to which
they were exposed because the probability of occurrence in a given year

was perceived as small. By changing the frame (lengthening the time

61

horizon and thereby increasing the likelihood that the homeowner would
experience the unfavorable outcome in the reference period) many people
altered their insurance coverage preferences. Kunreuther and Slovik
found that people look upon many forms of insurance as an investment.
By lengthening the time horizon. the attractiveness of insurance as an
investment was enhanced.

Kunreuther and Slovik also noted the propensity of consumers
to insure low cost, high probability events rather than high cost. low
probability events. This indicates that the loss of utility associated
with a relatively small material loss is more than the small amount of
utility gained (saving the premium) by not insuring and hence would
seem to conform to Tversky and Kahneman's hypothesis.

23 has examined the relationship

A series of recent articles
between risk aversion and the marginal utility of income. In the
economics literature. the curvature of an individual's utility function
has typically been associated with risk preferences. A utility
function defined over income which is concave (convex) is said to
indicate risk aversion (loving) in the individual. It has long been
recognized. albeit reluctantly. that this curvature contains
information about the marginal utility of income for the person in
addition to his risk attitudes. Krzysztofowitz states that the utility
function for an individual should be written as:

UN) = w(V(Y)) (3.7)

The function U(Y) encodes both attitudes toward risk and
strength of preferences while V(Y) measures strength of preference

(utility) only and W measures risk attitudes. By a clever structuring

of offers, Krzysztofowitz and others feel they can separate the

62

strength of preference component from the risk aversion component. The
specific structure of these offers is illustrated in Robison and
Fleisher and is summarized below.

Suppose a lottery will pay $1000 or nothing. with equal
likelihood.

How much would you pay for a ticket to play this lottery?

Let your maximum bid price be $400. Therefore the utility you get from
holding the ticket and the utility associated with $400 should be
equal. This can be expressed as:

0(400) - 1/2(U(1000)) + l/2(U(0)) . (3.8)
Suppose you are now asked the maximum amount you would pay to play each

of the two lotteries in Table 3.2. Most people will have a clear

 

Table 2: Two Lotteries
Lottery a Lottery b
Probability Payout Probability Payout
1/3 31000 2/3 $400
2/3 $0 1/3 $0

 

 

 

preference for lottery a or b so the maximum bid price for a ticket to

play one will exceed the other. However. the following manipulations

make clear that the expected utilities are equal. We can easily prove

that:
1/3(U(1000)) + 2/3(U(0)) = 2/3(U(400)) + 1/3(U(0)) (3.9)

To see that the equality holds. simply substitute the expanded

definition of U(400) from equation (3.8) into equation (3.9). multiply
and collect terms. The differences in the maximum bid price a person
would pay to participate in lottery a or b indicates a preference for

or an aversion to chance taking.

63

To separate risk aversion from changes in marginal utility
Krzysztofowicz derives the function V(Y). the pure strength of
preference. This is done by first bounding the choice set; 'What is
the worst outcome. what is the best outcome?‘ For example. consider a
struggling graduate student for whom the best outcome is a fellowship
worth $1000/month and the worst outcome is to remain penniless. We now
ask this hapless soul the point at which he is indifferent between
moving from $0/month to $X/month and from $X/month to $1000/month.
Let's say that for our poor student X is $450; implying that to go from
$0/month to $450/month is as satisfying to him as going from $450/month
to $1000/month. This process is continued. locating more points of
indifference by subdividing the range 0 to 1000 into ever smaller
components. A continuous, twice differentiable equation is estimated
over the locus of indifference points. The marginal utility of money
is said to be increasing. decreasing or constant if m(Y). defined

below. is less than. greater than or equal to zero. The quotient m(y)
2 2
m(Y) a -[(d V(Y)/dY ) / (dV(Y)/dY)] (3.10)

measures the degree of bending in the strength of preference function.
To determine the risk attitudes of an individual. Krzysztofowitz
compares the curvature of V(Y) with that of U(Y). The individual will
be risk averse (preferring) if U(Y) is more sharply concave (convex)
than V(Y). He expresses this property mathematically as:

n(Y) = -[<d2w(V(Y))/dZV(Y)) / (dW(V(v))/dV(v))1 (3.11)

If n(Y) is positive (negative) (zero) the person is relatively risk

averse (preferring) (neutral).

64

The ultimate contribution of this new technique is unclear
because it has not received wide-spread empirical testing. At a
minimum. it is a creative way of dealing with a problem that has been

largely ignored by researchers in the area.

Conclusions

The psychological literature. in general. lacks the rigor of
the economists' models. Economists have taken the route of

hypothesizing axioms of human behavior that would be observed in a

"rational” person. From these axioms. they have constructed some
rigorous and elegant models of choice under risk. Psychologists have
derived their axioms. not from some preconceived hypotheses of

rationality. but from empirical investigations into how people behave.
Some of these experiments involve hypothetical situations. some involve
actual behavior. Grether holds that the strengths of behavioral axioms
derived from experimentation are that they are real. well documented
and reproducible. It is important to bear in mind the questions raised
earlier by Ehrlich and Becker and by Robison and Lev regarding the
inadvisability of inferring risk preferences from observed behavior. In
addition. there is no clear route from empirical observations of human
behavior in risky situations to a theory. This reduces the generality
of the findings of psychologists.

The recent work done by Heiner. Krzysztofowitz and others
represents an important step forward, in my view. They are perhaps the
beginnings of a bridge connecting the economic and psychological
approaches to the study of behavior under risk. It is particularly

heartening to note that construction of this bridge is proceeding apace

65

from both sides of the gap that separates the two schools of thought.

The Approach Used in this Study

The approach taken in this thesis is a traditional economic
one. The reason for this is not that the misgivings voiced by
psychologists have been ignored or downplayed. Rather. the recent
work. as represented by Heiner and Krzysztofowitz. has concentrated on
microeconomic phenomena while a primary concern of this thesis is at
the macroeconomic level. It is unclear how one goes from the micro-
level behavioral descriptions of these recent works to macro-economic

results.

This thesis will. therefore. use a Mean-Variance model to ~

analyze the revenue insurance program. Details of this approach are
provided in the following chapter. The advantages of this approach are
an ability to aggregate results and its applicability to a large class
of decision makers. We turn now to a more detailed examination of the

theoretical models employed in this thesis.

66

. See Kunreuther and Slovic. 1978. for a brief discussion of this

distinction.

. This constraint is derived from the expected profit function

of the seller:
W = (1 - p)an — p[aF(A) - anl

where all variables are as defined in the body of the paper.
See Ahsan. Ali and Kurian. 1982. page 522.

Full insurance is coverage such that U'(Y1) = U'(Y ) implying that

Y c Y for concave utility functions. ' The subscripts refer to
the stage of nature.

. An actuarially fair price implies an exchange of p/(l - p) units

of income in state 1 for an additional unit of income in
state 2. given that state 2 occurs with probability p/(1-p).
See Ehrlich and Becker. 1972. page 626.

. Ehrlich and Becker. op. cit.. define insurance as

S = [0 - [0e

Where
8 = the amount of insurance purchased.
IO = income realized in state 0.
Ice = endowed or certain income in state 0.

Thus. if p is the price of insurance.

ds/dp = dIo/dp — dIoe = dIo/dp

since the endowed income will not change with a change in the
premium.

. Ehrlich and Becker. op. cit . page 637.

Ehrlich and Becker. op. cit.. page 626. They define the cost of
self insurance as negative one over the marginal cost of a loss
plus one:

= -1/(L'(C) + 1)

Since they have defined the loss function as the value associated
with the favorable state less the value associated with the
unfavorable state. the probability of occurrence doesn't affect the
cost of self~insurance.

. Ehrlich and Becker. op. cit.. page 637.

. Viscusi, 1979. page 1205.

67

10. Viscusi. op. cit.. page 1202 and 1205.

11. Adverse selection refers to the situation where only those
individuals who know they are likely to collect an indemnity
purchase insurance. In short. only high risk people buy
protection.

12. Moral hazard is the case in which the purchaser of insur-
ance has an incentive to allow the unfavorable event to
occur.

13. Heiner. 1983. page 561.

14. Heiner. op.cit.. page 569.

15. Heiner. op. cit.. page 577.
16. King and 0amek. 1983. page 18.

17. Coinsurance means that for losses above a given level. the
insurer and insured share losses according to some schedule.

18. von Neumann and Morgenstern. 1947. define rationality in a consumer
by postulating conformance to six axioms:
Orderability - consumers can rank the prferability of all
choices available.

Transitivity - if option a is preferred to option b and
option b is preferred to option c. then a
will be preferred to c.

Continuity - by altering the probabilities attached to
outcomes. indifference between any two
outcomes can be achieved.

Substitutability if a consumer is indifferent between
apples and oranges and the only
difference between two fruit salads is
that one has apples and the other
oranges. he will be indifferent between

the two salads.

Monotonicity - increasing the probability of a favorable
event increases the utility of the
decision maker.

Probability it is assumed that consumers accurately

and correctly use statistical data.

19. Tversky and Kahneman. 1981. page 455.

20. Maitel, page 197.

21.

22.

23.

68

Bayes Theorem is used to calculate conditional probabilities. A
conditional probability calculates the likelihood of an event
occurring given that we have information about which of numerous
possible states of nature will occur. It is used to revise beliefs
about the environment a decision maker faces.

Tversky and Kahneman. 0p. cit.. page 454.

See Krzysztofowitz 1983. and Bell and Raiffa. 1979. as examples of
this literature.

Chapter 4

A Theoretical Model of Revenue Insurance Demand

This chapter describes the expected value-variance (E—V)
model (and presents a graphical description of the revenue insurance
program. Then. using the E—V model. a mathematical model of insurance
demand is developed and interpreted.

Ag_§§pecteg Value-Variance Model

A E—V model describes action choices. or options available
to a decision maker. in terms of their expected values (P) and
variances . From the set of action choices available to the
decision maker. the expected value-variance (EV) frontier is formed.
To be a member of the EV frontier. the choice must have a smaller
variance (expected value) than all other options with the same expected
value (variance). Only points on the frontier are considered by a
decision maker. Figure 4.1 illustrates an EV frontier. Action choices
located in the lower left-hand portion of the quadrant are low mean.
low variance outcomes. In order to achieve a higher mean outcome. the
decision-maker must be willing to accept greater variability. Moving
to the right along the EV frontier. the trade-off between )1 and 02
is progressively less favorable in the sense that increasing amounts

of variability must be accepted for each additional unit increase in

69

70

u Edb

E-V Frontier

"ca

 

 

Figure 4.1: Equilibrium on an EV Frontier

the mean outcome. What is required for an optimum in EV space is
tangency between an isoexpected utility curve. (8(6)). for the
decision maker and the EV Frontier. In Figure 4.1 this equilibrium is
shown as point A- The intercept. "CE is the certainty equivalent
level of income. the level received with certainty that leaves the
decision maker as well off as all other points on 8(6). The curve
8(6) is not observable and is difficult to derive.1 Therefore. the
line BC might be used as a linear approximation of the isoexpected
utility curve. By requiring the line be tangent to the EV frontier at
A, the same solution is obtained from our linear approximation as from
the curve E(U). The point B is the intercept of the linear tangent and
approximates the certainty equivalent (#08) level of income. Since we
are in expected value—variance space. the formula for BC will be of the
general form:
n 2 CE + qoz (4.1)

Where a is some constant and CE is the certainty equivalent level of

71

income for the linear tangent. Fruend has shown that <1 is equal to
k‘“’/2 . a linear approximation of the Pratt—Arrow absolute risk
aversion coefficient.2 Therefore. if we can map the EV set and observe
the equilibrium point chosen by the decision maker. we can express the
approximation of the isoexpected utility curve, after rearranging
terms. as:
CE 8 fl - (X/2)02 (4.2)

We will call equation (4.2) the Certainty Equivalent expression.
Knowledge of the specific form of the decision maker's utility function
is not needed for this approximation.

Use of the certainty equivalent expression to analyze a
decision maker's optimal choice was thought to be restricted to cases
in which the decision maker's utility function was quadratic or when
the probability density functions (PDF) of the available action choices
were fully described by their means and variances. Neither of these
conditions is likely to hold in agriculture. yet the approach used is
justifiable because the error associated with EV set analysis will be
small if the distributions being considered are not highly skewed.
Furthermore. it has been shown both theoretically and empirically that
the EV set closely approximates the efficient set produced by second
degree stochastic dominance. What this means is that for all decision
makers whose utility functions are concave downward [U'> 0. U"< 0] the
EV set will contain the preferred action choice.

In addition. much of the criticism of E-V models has been
based on the fact that they are not consistent with Expected Utility
(EU) models. Given the criticisms of the EU models discussed in the

preceding chapter. it may not be appropriate to reject use of the E~V

72

model simply because it does not. in all cases. conform to a model that
many don't believe in the first place. As Meyer and Robison say. "if a
valuation function can be deduced which orders action choices over
means and variances in a manner consistent with our intuition and
experience. its usefulness should not be questioned simply because it

3 Meyer and Robison deduce a case in

lacks consistency with EU models."
which there is always consistency between the E-V and EU models. If
there is but one risky asset in the decision maker's portfolio and we
require the slope of the line BC in Figure 4.1 to increase. (remain
constant). (decrease) as the decision maker exhibits increasing.
(constant). (decreasing). absolute risk aversion. the E-V and EU model
results will always be consistent. This result derives from the fact
that with only one risky option. the EV frontier is composed of various
combinations of risky and safe assets. This means that the choice

which maximizes the EU model will. by definition. be a member of the EV

set.

A Conceptual View of the Insurance Option

Virtually all risk-reducing strategies work on the principle
of trying to modify a probability density function (PDF) of concern to
the decision maker. Insurance offers three basic types of
modifications. The deductible form of insurance. common in automobile
insurance policies. takes the probability of events worse than the
insured level and "piles" it at that level. In addition. the entire
distribution is shifted to the left by the amount of the premium paid
for coverage. This is shown in Figure 4.2. When facing a distribution

of output such as Figure 4.2, the decision maker with a deductible

73

insurance policy is assured of an outcome of at least x Should an

1-
OUtCOMB such as X2 occur. the insurer pays the insured an amount (x1 —
x2),
A second type of modification offered by insurance is termed
coinsurance. With coinsurance the insured and insurer share the cost

of unfavorable outcomes. If the purchaser has a coinsurance provision

Probability

 

 

 

Output

 

Figure 4.2: The PDF with a Deductible Form of Insurance

whereby she is liable for 25 percent of the value of lost output and
the insurer covers the other 75 percent. a loss of $200.00 means the
insurance company will pay her $150.00 and she will be responsible for
the remaining $50.00. Again, the entire distribution is shifted to the
right by the amount of the premium. See Figure 4.3 for an illustration
of how coinsurance changes the distribution.

The third form is a hybrid of the deductible and coinsurance
forms. A. policy with coinsurance above a specified deductible is

frequently used in medical insurance policies.

74

Probability

 

 

 

Output

Figure 4.3: The PDF with the Coinsurance Form of Insurance

Revenue insurance. as currently discussed. would be a
deductible type of insurance. It would be similar in form to the
current crop insurance program in that a fixed deductible. say $200.
will be replaced by a deductible that is a function of the mean level
of revenue over some historical time period. We will call the
deductible level in a revenue insurance policy the coverage ratio.
Suppose the average revenue over the past few years for farmer Jones is

$100,000 per year. With revenue insurance he could insure that his

gross revenue from farming will not fall below some proportion of this
amount. say $75.000. in the comming year. In exchange, Jones pays a

Premium. 1 . Figure 4.4 illustrates how a revenue insurance program

Would modify Jones' PDF over revenue.

75

       
 

 
 

 

 

Probability
I 1‘
’I I:
l I I
I I ’ '
/' I , '
’1' I, l
I
1 4 3 - Re venue
575,000-1 $75,000 $100,000

Figure 4.4: The Effect of Revenue Insurance for Farmer Jones

Purchase of the revenue insurance policy truncates the
revenue distribution at afl. In the Jones case. the mean, u . is
$100,000 and the coverage ratio. a. is .75. The entire PDF is shifted
to the left by the amount of the premium. I . All of the probability
that had been in the left-hand tail of the original PDF is accumulated
at the deductible level. $75,000. The mean of the truncated
distribution will be somewhere to the left of the old mean. If the
mean of the post insurance distribution remained the same (increased),
the buyer would receive as much (more) in benefits from the insurance
policy as he pays in premiums. While this may be the case for an
individual in a given time period. it cannot be true for the aggregate
of individuals across time periods. If it was true. the insurance
company would lose money and eventually go out of business. Insurance

Itill be expected to decrease the variance of outcomes.

76

A Mathematical Model of Insurance Demand

To model a decision maker's response to revenue insurance by
means of E-V model. expressions for the mean (I*) and variance (0%“) of
the truncated distribution are needed. Since the pre-insurance mean
and variance are known. the post-insurance PDF should be defined in
terms of these values. The new mean may be defined as:

A“ +-
III = (all - I: - 10]an + f (Y - c - 104(de (4.3)
0 a“

In equation (4.3). ‘K is the insurance premium. C is the farmer's non—
insurance costs and f(Y) is the probability density function over
revenue. All other variables are as previously defined. It should be
pointed out that equation (4.3) is in terms of income. not revenue.
The intuitive reason for this is the belief that farmers will evaluate
the revenue insurance program in terms of what it will do for their net
income position. In addition. the E~V Model contains the buyer's risk
aversion coefficient. Since this variable is defined over income, the
other terms in the expression also need to be in terms of income to
remain consistent.

Equation (4.3) may be interpreted as follows. The first
term to the right of the equality calculates the probability weighted
value of receiving the deductible level of income. The probability of
an indemnifiable event is multiplied by the minimum revenue the
purchaser will receive, a“. less the premium and non—insurance costs.
In the second portion of the equation the mean outcome over the portion
of’ the PDF not covered by insurance is calculated and costs and
premiums are again deducted.

To simplify the expression in (4.3). define the following:

77

afl
P =/f(Y)dY
0

and

+0
E(Y ) = *1 = / 'H(Y)dY
2 2 afl

The term P is simply the cumulative probability at a“ and Y is the
mean outcome above the point of truncation. Using these definitions.
Equation (4.3) becomes:
1* a aflP + Y - 1 - c (4.4)
2

To form the variance for the post insurance distribution.
recall that the variance of a linear combination of a variable x which
is of the general form a + a x. is simply a2 times the variance of x.
All constant terms whigh d6 not multiply Y in equation (4.1) can.
therefore, be ignored when forming the variance of the truncated

distribution.

Define a new variable Z with the following distribution:

a“ with probability P
2 a

Y with probabIlitY r(Y)

Therefore. the expectation of Z is:

5(2) = 3“ + Y
2

So the variance of Z is:

+-
02 :- (aunp + f Y2+('Y')dY - (aIlP + Y )2
Z afl 2

78

a (aF)2P(i - P) + (I - P)fl2 + 02 - ZaFY P ’ *2 (4.5)
2 2 2
Where
+0
02 = f Y2+<Y>d¥ - (1 - (mm
2 a“

In this model the insurance premium is based on the average
indemnity paid by the insurance company. The average indemnity may be
defined as:

- a“
i . j (all - 04mm
0
8 aFP - Y
i

The premium paid by a buyer will be defined as:
t I 9(aflP - Y )
1

Where

This simply says that the insurance company will charge the average
indemnity plus some percentage for the coverage it extends. The amount
by which I! exceeds 1 will be referred to as the loading factor. The
loading factor is designed to cover the insurance company's fixed and
variable costs. With this definition of I. the buyer's insured mean

income can be rewritten as:

1* = aHP + Y - V(aHP - Y1) ' C (4.6)
2

53ince the premium doesn't appear in the buyer's variance expression.

79

its definition doesn't change. Table 4.1 summarizes the properties of
1* and '°*3 with respect to the parameters in the model. Table 4.1
indicates that an increase in the coverage ratio. the loading factor.
the pre—insurance mean or other farm costs cause the mean of the post-
insurance income distribution to fall. The only unambiguous signs for
the variance term are with respect to the coverage level and the mean
outcome. An increase in the coverage level or the mean reduces the
variance. Intuitive explanations of the ambiguous signs will be
provided as part of the discussion of the E-V model. The mathematical
expressions from which these results are derived in Appendix 1.

Table 4.1: The Effect of Changes in Model Variables on the
Mean and Variance of a Farmer's Insured Revenue PDF.

 

Exogenous Sign of Sign of
Ugriabie 1* 0*2

a - -
v - (b)
C - (b)
p - -
Y ?(c) ?
2

 

 

 

a. Assuming a risk averse decision maker.
b. Terms do not appear in the definition.
c. ? = ambiguous.

80

Forming the Certainty Equivalent Expression

The expressions (4.6) and (4.5) are used to form the

certainty equivalent expression for an insurance buyer:

CE = aflP + Y - V(aflP - Y ) - C - (x/2)[02 +
2 i 2

(au)2<P(I — P)) - 2auY P + u2(1 - P) - Y2]
2 2 (4.7)

Having formed the certainty equivalent expression. what is the optimal
level of insurance to carry? Differentiating (4.7) with respect to "a"
and setting the resulting expression equal to zero. the optimal

insurance coverage is:

dCE/da = MP(1 - v - xiau(i - P) - Y J) = 0 (4.8)
2

So, at the optimal level of insurance.

0 8 1 - 7 - xtau(1 - P) - Y 1 (4-9)

Since the coverage level. a. is part of the definition for P

and Y it is difficult to solve for a*. the optimal coverage ratio.

2.
It is. however. possible to solve for the optimal loading factor. a
fact used in the empirical portion of this study. Furthermore. the
(expression in equation (4.9) can be used to determine how the coverage
ratio will change in response to changes in other model parameters by
implicit differentiation. For example. suppose there is an increase in
tin: loading factor. what will happen to the optimal coverage level? To

determine this. equation (4.9) is totally differentiated with respect

to a and v to get:

81

dZCE = [-X(F(1 - P))]da - (lid? = 0 (4-10)
or

(da/d!) = l/(-XF(l-P)) < 0

This result simply says that as the loading factor increases, the
optimal level of coverage will fall. Table 4.2 summarizes the
relationship between the optimal coverage ratio and the exogenous
factors in equation (4.9). The results indicate that as a person
becomes more risk averse. the insurance coverage sought will increase.
If the mean of the farmer's revenue PDF increases and the farmer is

decreasingly risk averse or risk neutral, the optimal coverage ratio

will fall. Decreasing risk aversion implies that as wealth increases
so does willingness to bear risk. This condition is expected to hold
for most people. The young person who has just graduated from

university is probably less willing to accept a fair bet of $100 than
he will be when he becomes the chief executive officer of a Fortune 500
company.

Finally. the ambiguity of a change in Y (and Y1 or P

2
as well) on the amount of insurance coverage sought can be explained
intuitively. Two cases will be discussed below. In both cases. the
mean of the pre-insurance distribution is held constant. This allows
us to concentrate on substitution effects. If decreasing or constant

risk aversion is assumed. the analysis that follows will not change

even if income effects are included.

82

Table 4.2: The Impact on the Optimal Level of Insurance of Changes
in the Factors Y , H, x, v.

 

 

2
Exogenous Sign of
ELCJLOP a
Y ?
2
X +
n 2(1)
' -

 

 

 

i. If the buyer exhibits constant or
decreasing risk aversion, this sign
will be negative.

Consider how an increase in the mean outcome above the

truncation level. Y2 . affects demand for insurance. Two scenarios are
possible for this mean preserving spread. An increase in Y2 could be
achieved holding P constant. This scenario implies that probability
may be shifted within the two parts of the distribution (the insured
and uninsured portions) but not between the two parts. This type of
change is depicted in Figure 4.5. In Figure 4.5 the a are all equal
indicating that the mean has not changed but a given amount of
probability has been taken from a region nearer the mean and moved

further into the tails. Another result of this change is a shift from

Y2 (Y1) to Yz' (Yl') as illustrated in Figure 4.5. As an example of

this type of shift. consider the following. Suppose trading
relationships between two countries have been disrupted. The buying
(country becomes erratic in its importation policies. Sometimes it

cones into the market in a big way. buys large quantities of
agricultural products and thereby creates a tight market in the
supplier country. Prices and revenues for farmers in the supplier

country rise. Just as frequently. however. the importing country buys

83

little. surplus stocks develop and prices and revenues fall.

What is the effect of this sort of change on the demand for

insurance? The model predicts demand will increase. The average
indemnity received increases in this situation. making insurance a
better buy. The environment facing the decision maker is riskier. in
the Rothschild and Stiglitz sense. This being the case. demand for

insurance should increase.

      
   

obability

 

’-----------------

p-O---------------------‘-.

 

)o-o-nuupuccqnnuccuupb

P------.a

 

 

'4
”“1
f
-<
9
as
C
I
‘
.c
NW
(1
-<
NU

Figure 4.5: A Mean Preserving Spread Holding P Constant

a
C
x. __ ‘ Revenue

84

In the second case. Y2 increases but P is no longer

constant. If P increases to P' as shown in Figure 4.6, demand for
insurance should increase since an increase in Y2 . holding constant.
implies a fall in the average outcome over the insured portion of the
distribution to Yl'. This means the average indemnity received
increases. Since the average indemnity is larger and the probability
of receiving it has increased. demand for insurance should rise. Such
a change might result from weather patterns that become more variable.
Another explanation might be the existence of moral hazard. Suppose for
example. a farmer sees that his crop is doing poorly because of weeds
or insect damage. He might find it economically advantageous to forego
the expense of applying herbicides or pesticides and collect on his
insurance policy instead.

It is also possible that P decreases while Y2 increases.
This sort of change will have an ambiguous effect on demand. While the

average indemnity will still increase. since Y falls. the probability

1
of receiving a payment decreases. Figure 4.7 illustrates this
scenario. A situation causing this type of shift might be a change
from a highly specialized farm to greater diversification. With
greater diversification. more probability will be stacked in the
central portions of the PDF since to be in either tail. revenues from

all sources have to fall or rise simultaneously. By implication,

less probability is left in the tails since it is less likely that

85

Probability
l

P<P'

  

 

\
\

 

 

3------
)

Revenue

C
l
A
v-<

Nu.---------------------. --------

Vi, + Y? ”H

G
04
MG

Figure 4.6: A Mean Preserving Spread. P and Y2 Increase.

revenues from all crops would be perfectly correlated. However. if all
revenue sources on a diversified farm do experience low revenues in a
given year. revenues might be expected to fall vis-a-vis the
specialized farm which is taking advantage of economies of size more
completely. As argued above. it is unclear how diversification would
affect demand for insurance because of the countervailing impacts of a

higher average indemnity coupled with a lower probability of a pay—out.

86

   

 

 

Probability
I
I
I
P I
/ I
I
/ l
I
p' /: I. I
/ '
,.<’ I
- o/' i '
A. .... / I I 1 Revenue
VI. * y? au_, u_, Y? e Y3.

FIGURE 4.7: A Mean Preserving Spread. P Decreases and Y2 Increases,

Because of their interrelationships. similar arguments hold

for changes in P or Y1 The conclusion is the impact on demand for

insurance caused by changes in P. (1 - P). Y1 or Y2 cannot be

predicted without knowing the nature of the changes involved.

The mathematical expressions for the relationships between

changes in model parameters and optimal insurance coverage are provided

in Appendix 2.

W

This chapter has derived the demand for revenue insurance in

the context of a E-V model. While most of the model results conform to

intuitive expectations others were more surprising. In particular. it

87

was discovered that the effect of a mean preserving shift that changes
Y1. Y2. or P is ambiguous. At a minimum. the specific type of shift
involved must be known in order to predict the impact on insurance
demand. In some cases knowledge of the characteristics of the shift
will not be sufficient to allow us to predict the direction of change
unambiguously.

A number of interesting policy implications can be drawn
from the results of this model. First. as expected. an increase in the
loading factor charged will be likely to cause a farmer to decrease the
level of insurance coverage he purchases. The loading factor might be
increased if the nonindemnity costs of the revenue insurance program
increased. The inclination of the insurer would be to increase the
amount he charges if his own cost of doing business increases. If the
negative relationship between the coverage level and the loading factor
is sufficiently strong the economic position of the firm could
deteriorate if the loading factor is increased. Furthermore. there is
the additional consideration of portfolio effects to consider. An
increase in the loading factor could drive those buyers who pose the
least threat to the economic viability of the insurer out of the
insurance market.

It was also shown that an increase in the buyer's risk
aversion coefficient would be expected to increase the coverage
demanded. An increase in the risk aversion of a buyer could be caused
by a number of factors: a revision of his subjective beliefs about the
revenue PDF he faces. a deterioration of his equity position. and so
on. For example, a farmer in the U.S. Corn Belt may, as a result of

last year's drought. believe weather patterns are going to be

88

unfavorable over the next few years. This may lead him to increase the
the level of insurance protection sought. Because he believes the
riskiness of the environment has increased, this farmer would like to
allocate more of the risk bearing responsibilities to the insurance
company.

Another interesting conclusion growing out of the
theoretical model is that with decreasing or constant risk aversion an
increase in the mean of the pre—insurance revenue PDF will. ceteris
paribus. cause the coverage level sought to fall. In practical terms
this implies that an increase in the wealth of a farmer will reduce the
insurance coverage sought. Since younger farmers are likely to have
less wealth. the expectation would be that younger farmers would be
more attracted to this program than older. wealthier farmers. If
revenue insurance increases the ability of a farm to weather a bad year
or two. this higher level of demand from younger. poorer farmers could
have important implications for the structure of farming.

Finally. the rather extensive discussion of how a change in
Y1. Y2. or P might affect demand for revenue insurance highlightsf the
importance of changes in the characteristics of the revenue PDF on

demand for insurance. Many of the changes discussed could result from

changes in government policies (ie. trade policy) or individual
incentives (ie. moral hazard). These results indicate that the success
or failure of a revenue insurance program depends heavily upon a
variety of human actions. not all of which are directly dependent upon
the revenue insurance program per se.

Having gained a greater appreciation of the complexity of

insurance demand. it is now time to turn to an examination of insurance

89

supply. It is on the supply side of the market that many of the more

pressing questions about revenue insurance are found.

 

1. See Tversky and Kahneman. 1981. for a discussion of some of the
difficulties encountered when trying to derive the utility
function of an individual facing uncertain action choices.

2. See Pratt for a discussion of the absolute risk coefficient.
defined as

RIF) = “U"(F)/U'(H)

R(u) is a measure of a decision maker's aversion to risk. A
positive value for R(u) indicates risk aversion. The attraction of
R(u) is that it is a unique measure of a decision maker's risk
preferences. This has distinct advantages over the use of an
estimated utility function to determine the decision maker's risk
preferences since an estimated utility function will provide a
unique and consistent ordering of preferences up to a positive
linear transformation only. Using R(u) allows transformation of
the estimated utility function in any fashion and still obtain the
same ordering of preferences.

3. Meyer J. and Lindon J. Robison. 1984, page 3.

Chapter 5

A Theoretical Model of Insurance Supply

Insurance works because the insurance seller can pool the
risks faced by a large number of people and take advantage of
experiences that are not perfectly positively correlated. Less than
perfect positive correlation means there will be occasions when the
seller does not have to pay indemnities to all his clients. The
insurance company uses the premiums from buyers who did not suffer an
indemnifiable loss to off-set the benefits it extends to buyers who
did. For this reason. a model of insurance supply must include
multiple buyers. In this chapter the E-V model developed in Chapter 4
will be extended to include multiple buyers and one seller. The
results of this aggregate model will provide the basis for predictions

about the macroeconomic impacts of a revenue insurance program.

13e7§gpply of Insurance

Three factors determine the workability of insurance. The
three. discussed earlier. were (1) the extent to which hazards are
correlated. (2) the number of participants in the insurance pool and
(3) the quality of the data. A measure of the extent to which hazards
are correlated is included in the supply model by means of the
correlation coefficient. The seller would like the correlation
coefficient to be strongly negative. If it is. the probability that
its clients will simultaneously experience outcomes that make the
insurer liable for payouts will be low.

Correlation. of course. requires more than one buyer, In

90

91

addition. the underlying principle of insurance is that pooling risks
enables individuals to achieve protection from catastrophic outcomes
for less than it would cost them to self—insure. This is possible only
when a large number of buyers with uncorrelated hazards purchase
insurance.

The issue of data quality is tremendously important for the
design of an actuarilly sound revenue insurance program.
Unfortunately. it is not an issue the models to be built will be able
to consider. at least directly. The data issue will be discussed more
extensively in Chapter 6. where the empirical portion of this

investigation is described and discussed.

A Market Model of Revenue Insgrance
The seller's costs and returns are. in essence. the opposite

of the buyer's. For a buyer. the purchase of insurance means he is no

longer as concerned about outcomes below his deductible level since he
will. after receiving his indemnity. always get an dollars. The
seller. on the other hand. is concerned with precisely this region.
Figure 5.1 illustrates the revenue expectations for the insurance

seller. Below the deductible level for a given buyer. the seller earns

the premium less the indemnity paid to the buyer. Above the deductible
level the seller earns the premium. Costs other than indemnities have
to be paid regardless of the client's experiences so the entire
distribution is shifted to the left by B. These nonindemnity costs are

assumed to be constant.

92

Probability

 

‘\
‘ p—-———-—\-——--

    

\

’

 

  

I
I
I
k f
I
I
I
' Seller's Revenue

I A

1 - (an? - Y1) - 8 1-8

 

Figure 5.1: PDF of Seller's Revenue from a Given Buyer

Figure 5.1 illustrates the seller's revenue experience with
one buyer. Each of its n clients. where n is some large number. will
generate its own unique revenue history for the seller. We can picture
a series of figures such as the one portrayed in Figure 5.1 with some
PDFs stretched and others contracted. Figure 5.2 depicts three such

PDFs.

93

Probability I

 

 

 

 

Seller's Revenue

Figure 5.2: The PDF of Returns to the Seller from Three Buyers

The seller's total return in any given period will be the
sum of the premiums collected from its n clients less the payments made
to the subset of buyers who experience indemnifiable losses less the
non—indemnity costs. Since neither the number of clients to *whom
benefits will be paid. nor the size of these benefits is fixed. the
seller's return in a given period cannot be known with certainty. Over
time and with a large enough pool of buyers. however. both of these
variables can be predicted with a high degree of accuracy if the
conditions producing the PDFs pictured in Figure 5.2 are stable or
change slowly. It is the stability of these relationships that allows
an insurance company to develop the actuarial tables that predict the

likelihood of hail devastating the corn crop on a farm in Huron County.

94

Michigan or of an American male. sixteen years of age. having an
accident in his sportscar.

The returns to the seller will vary from period to period.
The amount of variability experienced by the seller will be a function
of the variability experienced by its clients and the extent to which
this variability is correlated across buyers.

In the next section mathematical expressions are developed

for the seller's expected returns and the variance of returns.

A Metheggtical Model of Insurance Supply_
The expected revenue of a seller with n buyers can be

expressed as:

S n
E(R ) a (X I - (a H P - Y )) - B (5.1)
i=1 i i i i ii
n

I (X (I - i)(a H P - Y )) - B (5.2)
i=1 i i i i ii

Where:

I a Premium for buyer i.

9 a The loading factor for buyer i.

a 8 Coverage ratio chosen by buyer i.

u a Mean outcome for buyer i.

P 8 Probability in the insured portion oi buyer i’s revenue
i PDF.

Y I Average outcome of buyer i over the insured portion of
1i the PDF.

8 a Fixed costs.

Equations (5.1) and (5.2) describe mathematically the

expected revenue of the seller that was described in prose in the

previous section. Equation (5.1) indicates that the seller's expected

95

net returns will be the premium charged less the average indemnity for
each of its n clients. less non-indemnity costs. Equation (5.2) uses
the definition for the premium developed in Chapter 4.
v.(a H P.- Y. i . to simplify the expression for expected returns.
The substript; in the equations refer to the individual buyers in the
insurance pool.

Because the very general form of the model described in
equation (5.1) is not mathematically tractable. several simplifying

assumptions are employed. It is assumed that the mean and variance of

each of the n buyers are related in the following way:

F 8 a u
i i 1
and
02 8 a2 02
i i l
where
0 < a < a
and
a 8 i

i
This formulation assumes that the PDF of all buyers in the

insurance pool can be described as a stretched or contracted version of
some given PDF. It indicates also that when the average outcome
increases, the variance of outcomes also increases. Finally. this
assumption implies that the probability in the insured portion of the
distribution is the same for all farmers. This is shown in Figure 5.3
where the cumulative probability. P, is the same for both buyers but
the average indemnity (app - Y ) for buyer one is a stretched version
of the average indemnity for buyer two. The amount of stretch is
measured by the a factor. A test of the degree to which this
assumption accurately describes the farming population will be

performed in Chapter 6.

96

Probability

 

 

 

Seller's Revenue

 

 

aul
Figure 5.3: The PDFs of Two Buyers.

Where
a (afl - Y ) a a“ - Y
1 2 21 1 ii
Given the above definitions for the mean and variance, and
the definition for the loading factor (see equation (4.9) in Chapter

4). the loading factor for buyer 1 is defined as:

val-xa(afl(l-P)-Y) (5.3)
i i l 2

This means that the loading factor for each client may be different.
either because his risk aversion coefficient or his stretch factor is
unique.

The model will be further constrained by the following

assumptions:

97

a = a
i 1
C = (1C
1 i 1
for
i = 1. , n

Neither of these assumptions is severely restrictive.
Assuming all buyers are offered the same level of coverage is likely to
describe how the actual revenue insurance program will operate. This
is, for example, similar to the way the Federal All-risk Crop Insurance
program currently works. The assumption that non-insurance costs are
also adjusted by the stretch factor. a , indicates that higher level

mean outcomes are only achieved by increased expenditures.

The Expected Value-Variance Model for the Insurance Seller
The seller's expected return was defined in equation (5.1) as
the premium collected from each of its n clients less the sum of the
average indemnities paid to those clients and non—indemnity costs.
Given the simplifying assumptions detailed above. the expected revenue

for the seller is written as:

S n B
E(R ) I [2 (1 - x d (afl(i - P) - Y ) - i)(¢ (aFP - Y ))l - B (5.4)
i=1 i i 2 i i
n B
= (aHP - Y )(Y - afl(i - P))(X «2x ) (5.5)
1 2 i=1 i i

The superscript B on X indicates this is the buyer's risk aversion
coefficient.

The variance of the seller's revenue is, as might be
expected, a more complicated expression. To derive an expression for

the seller's variance note that the expected returns for the seller

98

from the ith buyer is:

S a“ . m o..-. .
EILR > a f (It - (all - Y > - B>+<Y>dY + j (1 - 3)“de
i 0 i i i a“ i
3 1i " (all P ‘ Y ) ‘ B
i i ii

Following the pattern developed in Chapter 4. a new variable Z1 is

(5.6)

defined as:
Y with probability {(y)
' 8 ii
a“ with probability (1 - P)
i

Therefore. the expected value of Z1 is:

i ll 1

Which means that the variance of the seller's revenue caused by the ith
buyer is:
Uar<B ) = Y 2 + (afl )2P(1 - P) - 2a“ Y (i - P) + 02 + “2P (5.7)
i ii i i i1 ii i
Given the definitions for the mean and the variance. equation (5) may
be simplified to:
VariBi) = a_(Y2 + (a<)2P(i - P) - ZaHY fl - 9) + 02 + uzp (5.8)
I 1 i 1
As discussed above. the total variance of the seller will be equal to
the sum of the variances associated with each of the n buyers plus two

times the covariance matrix. This is expressed as:

S n n n
Uar<R ) a z 0*2 + 2(2 2 p 040*) (5 9)
i=1 i (=1 J=i+i ii i J
n 2 n n
= 0*ZIX a + 2(X x p a a )1 (5‘10)

1 I=l i i=1 j=I+1 ii i J

99

Where,

9 a the correlation coeiiicient for buyers i and i.
IJ

Therefore, the certainty equivalent expression for the seller is:

S n 8
CE = (aup - v >(Y - auci - P))(Z «ax )
1 2 i=1 i a
S n n n .
- (i/2)Io*2rx «2 + 2(2 2 p a a )1) (5-11)
1 i=1 i (=1 I=i+1 ii i J
Where
8

A = the seller's risk aversion coefficient.

100

Optimization in the Seller's Market

What is the optimal coverage ratio for the seller to offer
his pool of clients? To answer this question. simply differentiate
equation (5.11) with respect to "a" and set the resulting expression

equal to zero.

3 n B
dCE /da = 0 = [flPiY - au(1 - P)) - “(1 - P>(aflP - Y )1(X ask )
2 1 I31 i i
S n n n
- x [(afl2P(1 - P) - FY (1 - P))(2 «2 + 22 X a a P )
1 i=1 1 i=1 J=i+1 i 1 i1
n n
+ (0*2)(X X a a (29 /2a))1 (5-12)
1 i=1 J=i+1 i J ij

If the expression (BPij /2a) is not equal to zero the implication is
that the purchase of insurance causes a change in the pattern of
outcomes across farmers. One explanation for such a change would be
moral hazard. If the insurance policy caused farmers to take less care
of their crop when it looked as though it was not going to produce well
or when the market price was very low. 9“ night increase when
insurance coverage is increased. If the inciease in the correlation
coefficient is sufficiently large and positive. the expression in
equation (5.12) will always be less than zero. implying that no optimal
coverage ratio greater than zero would exist for the seller. In any
case. if the correlation coefficient is positively related to the
coverage rate. the optimal amount of insurance a seller will offer will
be reduced relative to the case in which these factors are independent.
For the moment. assume (apii /2a) {3 equal to zero.

Again. it is difficult to solve equation (5.12) for the optimal

101

coverage ratio because this ratio appears implicitly in so many terms
in the equation. To determine the relationships between optimal
coverage offerings and the other model parameters, equation (5.12) is
totally differentiated. The results of these differentiations are
summarized in Table 5.1 and the equations from which the results are

derived appear in Appendix 3.

Table 5.1: Changes in Optimal Coverage Offerings with Changes in Model

 

Parameters
Differential Sign

B

da/dx +
i

da/dfl ?

da/dY ?
2

da/da ?
i
S

da/dk ‘

da/dP ‘
ii

 

The signs of the derivatives in Table 5.1 are intuitively
appealing. An increase in buyer i's aversion to risk will increase the
seller's expected return (by increasing the loading factor) while
leaving the seller's variance unchanged. Assuming the seller has
constant or decreasing risk aversion. this will induce the seller to
increase the coverage ratio offered. If. on the other hand. the seller
becomes more risk averse or if the degree of correlation across
clients' outcomes increases. the coverage ratio offered would be
expected to fall. An increase in the seller's risk aversion or the

correlation coefficient focuses its impact on the variability of

102

returns. the first by increasing sensitivity to variability of returns
and the second by increasing the magnitude of variability.

The ambiguity associated with a change in a. stems from
its effect on the PDF of the seller's returns. An increase in a.
causes both the mean and variance of the seller's returns to increase:
It cannot be known, a priori. how the seller would react to these
changes. Similarly, an increase in )1 results in a larger mean and
variance for the seller's return. Again. the sign of this derivative
cannot be known without more information.

The reason an increase in Y2 will have an ambiguous impact
on the optimal coverage ratio offered is somewhat more involved. First.
assume the increase in Y2 is achieved without increasing n. This is a
situation analogous to the two cases discussed in the previous chapter.
Suppose. for example. that Y2 increases because probability is
shifted from the insured portion of the POP into the uninsured portion.
This could be in response to the development of a new corn cultivar
that performs better under a wide variety of conditions than do
existing varieties but does worse under certain extreme circumstances.
The shift in an adopting farmer's PDF resulting from this new variety
is illustrated in Figure 5.4. From the seller's point of view. such a
shift will increase the average indemnity paid but decrease the
probability of paying out such a benefit. The seller's response to
this sort of event will depend upon an intricate interplay of several
factors: the loading factor, the risk aversion of buyers and seller
and the correlation coefficient. An increase in Y2 has an

ambiguous impact on the loading factor because an increase in Y could

2

cause the difference aM(1 - P) - Y to rise or fall since P and Y2 will
2

103

both be changing. An intuitively appealing argument for the ambiguous

effect of this type of increase in Y on the optimal loading factor is

2

relatively straightforward. As long as u is held constant. an increase
in Y2 implies Y1 must fall. From the buyer's perspective this means
an increase in the average indemnity he will receive. However. since
P has fallen, the likelihood of receiving a payment is reduced.
Because these two factors exert pressures in opposite directions. the

optimal loading factor may increase or decrease when Y increases and P

2
falls. Since the buyer's behavior is uncertain. the seller's response
is as well.

Finally, how does an increase in Y of this sort affect the

2
correlation coefficient? If this new variety reduces the importance of
management decisions, the outcomes of farmers might be more highly and
positively correlated. Such an effect would put downward pressure on
the coverage level offered. In short, because there are a number of
potentially countervailing factors associated with an increase in Y2
the sign of the derivative (da/de) is uncertain.

104

  

 

Probability

   

P>P'

..---‘-...---.------ .-.

 

'----..--------.

Seller's Revenue

 

'4

'
Yi‘ 1

Figure 5.4: The Effect on the Seller's Revenue of a Shift in
Buyer i's PDF in which Y2 Increases and P Decreases

Conclusion

This chapter has presented an aggregate model of insurance
supply that was deduced from results of a microeconomic model of
demand. As far as I know, this is the first time this has been done.
The advantage of this procedure is that the two sides of the insurance
market are connected in a much more realistic manner than in most
market models. In conventional models the assumption tends to be that
as long as the seller is offering his product at a price that equals
his minimum average cost, he can sell an unlimited quantity. The
seller's sole motivation is assumed to be the maximization of profits.
Neither of these assumptions is realistic. The models deduced in this
dissertation assume that it is not only the level of expected revenue
that is important to a decision maker. but its variability as well.

Furthermore, the actions of buyers and the seller are related in

105

important ways.

-This procedure determines the reduced form equation of
insurance supply. From this equation the relationships between the
cost of insurance and model parameters were derived. The relationships
deduced from this aggregate model highlight the fact that the seller's
behavior in the insurance market is heavily dependent upon the behavior
of its clients. For example. it was noted that if the correlation
coefficient increased substantially when the coverage ratio increased.
the seller might cease to offer insurance. To the extent that the
program suffers from problems of moral hazard or adverse selection, the
correlation coefficient of the insurance pool will increase. Both
moral hazard and adverse selection are dependent upon the actions of
buyers.

It was also found that an increase in the average indemnity

paid (caused by an increase in Y holding u constant) will not

2.
automatically cause the seller to decrease the coverage offered its
buyers. The seller's response will depend upon the type of shift
involved. This is the seller's equivalent of the lessons learned in
the previous chapter regarding buyer response to an increase in Y2.
This result is particularly interesting in view of the fact that many
are concerned that a revenue insurance policy might induce producers to
take more chances in their operations. If this turned out to be the
case, the expectation would be that the variance of the farmer's
revenue would increase. In this model this type of change is

represented by an increase in Y holding fl constant. The initial

2

reaction is probably that this would cause the seller to decrease

coverage. increase the price charged or both. This model predicts this

106

will not necessarily be the case and will depend upon the nature of the
shift.

These results illustrate the interdependence between buyer
and seller in the insurance market. A seller's freedom to manipulate
the loading factor he charges a client is circumscribed by the coverage
level chosen by the buyer. The buyer's optimal coverage level is. in
turn, dependent upon the loading factor he is charged. This emphasizes
the point made by Hey regarding the intrinsic interdependence of
supply and demand in an uncertain world. As Hey puts it.

"We see immediately that unlike the conventional
(certainty) theory. we have a problem of consistency: the
optimal behavior of the buyers depends upon what the sellers
do; the optimal behavior of the sellers depends on what the
buyers do. It is no longer possible to analyse the two sides
of the market separately. and then 'bolt them together' to

get a market model. (author's emphasis) The behavior of the
sides must be considered simultaneously.

 

1. Hey .1979, Page 173

Chapter 6

An Empirical Test of the Theoretical Models

The models developed in this dissertation are based on a
theoretical model of insurance demand. It is crucial that the models
be tested for real world applicability and correspondence. This
chapter describes the empirical tests to which the models were put and
the results obtained.

The Empirical Model

The basic nature of the empirical test was to see if the
model could accurately predict willingness to pay for insurance
coverage. The willingness of a farmer to pay for insurance coverage is
a function of the cost of the coverage. the value of the coverage (in
terms of the frequency and size of indemnities received) and the
individual's risk bearing propensities. Each of these parameters would
be expected to vary from farmer to farmer. To facilitate the empirical
phase of this study a computer program was written to calculate the
premium each farmer should. according to the theoretical model. be
willing to pay. The program is available from the author upon request.
A portable computer was taken to each farm in the sample. data from the
farm were entered and the respondent asked if he would be interested in
acquiring a given level of protection at the stated price.

The model actually used in the field test was subsequently
reformulated. The discussion to follow will focus on the reformulated
model. The data from each sample farm were used in the reformulated

model to generate new estimates for the premium predictions.

107

108

In the empirical phase of the study the coverage ratio was
assumed to be set by the government at .5. .6 or .75. In Chapter 4. the
premium was defined as:

t = w taHP - f Ea

i i 1 a
If the coverage level is set. the choice for the farmer becomes, "How
much would I pay for a given level protection. or. alternatively. would
I participate if the premium was such and such?"

In Chapter 4 the optimal loading factor for a given farmer
was defined by the equation:
8
9 = l - A a (aflil - P) - Y )

i i i 2

Values for the parameters used to calculate the loading
factor and the premium were derived for each farm. The premium
forecast by the model could be more or less than an actuarially fair
price if the individual's loading factor was more or less than one.
Therefore. to determine the willingness of farmers to pay an amount
that would just cover indemnities. the actuarially fair premium was
also calculated. To calculate the premium required to just cover
indemnities the probability weighted average payment received by a

farmer. (aflP — 1 ) was calculated.
1

A flow chart of the computer simulation program is presented
in three parts in Figures 6.1. 6.2 and 6.3. In the first part of the
program. illustrated in Figure 6.1. data are entered into the computer.

The data required are the number of acres worked. the gross receipts

109

from farming and the adjusted gross receipts (taxable income) for each
of the ten years used as the base period. Gross receipts are converted
to a per acre figure to eliminate the effect of changing farm size on
gross receipts earned. Subsequently. both gross receipts and adjusted
gross receipts per acre are converted to constant 1983 dollars. These
real dollar/acre figures for revenue and income are multiplied by the
number of acres in production in 1983 to generate PDFs for these
variables for the farm's current size. The minimum and maximum revenue
and income levels are then located by the program. The differences
between the minimum and maximum revenue and income levels are each
divided into five cells of equal size. Revenue and income histograms
for the farm are generated by searching over the ten years of data and
placing each revenue or income value into the appropriate cell. The
the mean and variance of the income and revenue distributions are

estimated from these histograms.

110

Peres in Year I] Frees lssssus in Year :1 [lat Income in YesrTl
4

Grosslmvume

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fer Acre is
Y“! ‘ u
Oars-t Dollar
Sebmtime
[1. I
Mimi- lea]. Mimi- Isa).
”vanes Per Acre income
Maxi- lea]. Maxi- Real
lemme Per Acre Income
1 l
Elston-z lea]. Histogram:
[avenue Per Acre Real Income
1: Acres worked.
[983

 

 

 

 

 

I
Gaetate u 6 s2 Gemerats Choices
for Estimated 1

Figure 6.1: Part 1 of Computer Simulation Flow Chart — Data Entry and
PDF Estimation.

 

 

 

 

 

 

 

[ Estimating x 4___]

 

 

 

Generate Cluoose I! IF
Distributions A or I A I

 

 

 

 

 

 

tr 5th Generate
Choice New A

 

 

Mimi— Values
in lat-dill .
Distributions
e e
E

Estimate for
i Mimi-

 

 

 

 

 

 

Estimate for
3 Maxim‘-

 

 

 

 

 

Generate 3 Values

Between 1 Minim-
and 1 Maxim:-

Find "'1" (1-1.2)
Closest to st

 

 

 

 

 

Figure 6.2: Part 2 of Computer Simulation Flow Chart — Estimation of
the Farmer's Risk Aversion Coefficient.

lll

 

 

Choose Coverage Loved

I

Estimate P. Y1. Y2. 6 u
From Revenue Histogram
I

F
'L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I L
Estimate Estimate Estimate
Till to Average Pro-it-
Payout Payout - V(auP-Yl)

° UP - auP-Y1
_[
Hould You Pay:
Model Premit- l

 

Model Premium 2
Actuarial Premiu-

 

 

 

 

 

Uhat is the Maxi-
That You Mould Pay?
f
F

amine Another
Coverage Level

mg ‘3“

Figure 6.3: Part 3 of Computer Simulation Flow Chart - Premium
Estimation.

 

 

 

 

 

 

 

 

 

 

 

 

In the second portion of the program. Figure 6.2. the
buyer's risk aversion coefficient is estimated using the interval
approach. The use of hypothetical distributions in eliciting risk
coefficients has been criticized by numerous authors on a variety of
grounds. Robison (1982) summarizes many of these complaints and
concludes that despite the criticisms. the approach is a useful. albeit
imperfect. predictive tool. To implement the interval approach. a
series of choices between two distributions. each with six possible
outcomes. is generated. An example of a choice pair appears in Table
6.1. The numbers in each distribution are described as levels of
income the farmer could receive if he adopted an unspecified farm plan

(A or B). Each value in a distribution is equally likely to occur.

112

In the actual survey. it was suggested that the farmer imagine he had
one die in his hand and. having chosen a farm plan. he would roll the
die. If a one resulted he would experience the first value in his
chosen column (his chosen farm plan). a two meant he would get the
second value and so on. Thus. if a farmer faced with farm plans A and B
in Table 6.1 chose A and rolled a 4. he would receive $93,750 from
farming in the current period.

In each pair of distributions the range of outcomes in
choice B was twice that of choice A. The range of outcomes in Plan B
represents the range of the farmers' actual income experiences over the
base period. In the initial pair of distributions, such as the one
listed in Table 6.1 and pictured in Figure 6.4. both farm plans have
the same expected value. Based on the preference indication of the
farmer the values in distribution A are recalculated and the decision
maker is presented with another set of choices. For instance. if Plan A
in Table 6.4 was selected. a new set of numbers would be generated for
which the expected value would be less than that of Plan B. This new
option. call it Plan C. would have a minimum value of $40,625, a

1 Intermediate values will

maximum of $103,125 and a mean of $71,875.
be placed at equal distances between the minimum and maximum. Plan C
is less attractive than Plan A since the range is the same but the
expected value is smaller. Based on the decision maker's preference
for Plan C or B. the values in Plan C will be revised upward or
downward. We are searching for a point of indifference between the two
distributions. Since the interval method cannot locate the precise

point of indifference. we search for the interval that contains this

indifference point.

113

Table 6.1: Two Hypothetical Choice Distributions for Use in
Calculating the Risk Aversion Coefficient of a Farmer.

 

 

 

 

 

 

 

 

 

Plan A Plan B
Income Per Year Income Per Year
56250 25000
68750 50000
81250 75000
93750 100000

106250 125000
118750 150000
Probability
:
:
I
I
l
I
I
O
I
i
I
1 Revenue
a b H c d

(25000) (56250) (87500) (118750) (150000)

Figure 6.4: Two Distributions Used to Locate Indifference Points.

114

Figure 6.5 illustrates the choice tree faced by the buyer.
Each choice node will bisect the remaining risk aversion space.
Proceding out the ladder the range of values the decision-maker's risk
aversion coefficient could take is progressively narrowed. Each farmer
was presented with 5 pairs of distributions. The first four choices
took the farmer to the final rungs in the ladder. the fifth choice was
a consistency check. If the consistency check was failed. the interval
expected to contain the risk aversion coefficient was doubled. For
example, suppose a farmer opted for A. C. F and A in his first four
choices. The fifth choice would again be between A and F. If the
farmer now indicated a preference for A. the interval containing the
risk aversion coefficient would go from L to R. If he again chose F.
it would be from L to F. From this interval high and low estimates for
the risk aversion coefficient were generated.

The number of choices offered to farmers in the interval
approach will dictate the amount of Type 1 or Type 2 error contained in
the estimate of the risk aversion coefficient. If few choices are
offered. the likelihood that the decision maker's true risk aversion
coefficient will be contained in the interval is quite high but the
size of the interval is large. A large interval for the risk aversion
coefficient means that the high and low bid price estimates for the
insurance premium will be relatively far apart. If many choices are
offered. more precise estimates of the farmer's risk aversion
coefficient and bid prices are obtained but the likelihood of
containing the true values of these variables is reduced. Based on
pre-tests and the findings of King (1979). four choices were deemed to

offer the best trade-off of these two types of error.

115

Numerical values for the risk aversion coefficients were

estimated using the following formula.2

-kd -Xa -k((d-a)/2)

b = (-1/2k) * (e - e )/(e - 1) (6.3)
Equation (6.3 ) assumes the utility function for an
individual can be represented by a negative exponential equation. At
the point of indifference between two distributions the utility
associated with a distribution over the range "a" to "d" is equal to
the utility of the distribution running from "b" to "c". In Figure 6.4.
indifference between the two distributions shown would indicate risk
neutrality. If the values of "b" in the distributions that bound the
farmer's point of indifference are less (greater) than those in Figure

6.4. the farmer is said to be risk averse (preferring).

It is probably impossible to solve directly for x in
equation (3). Therefore. to obtain estimates for the two risk aversion
coefficients that bound the indifference point. a look-up routine was
incorporated into the computer model. To begin this routine. recall
that the certainty equivalent expression was:

CE = u + (x/2)02
Which means that

A = 2*(ifl - CE)/02) (6.4)

The minimum value in the distributions bounding the
indifference point for the most risk averse individual will be "a" in
Figure 6.4. Furthermore. for the most risk preferring person the
minimum value in the bounding distribution would be no greater than

the mean. These limits on the risk aversion coefficient correspond to

116

concepts in the Game Theory literature. A person who would be
indifferent between a distribution ranging from "a" (u)to u ("d") and
one ranging from "a" to "d". is said to be a minimax (maximin) type of
decision maker. A minimax (maximin) decision maker will always choose
the distribution offering the smallest (largest) possible loss (gain).
As this bounds the risk characteristics of the population. this range
will contain the true risk aversion coefficient of our farmer.

By substituting "a" and u for CE in equation (4) the
range over which the computer must search for the individual's risk
aversion coefficient is determined. One hundred values for x spaced
equally over this range are generated. These 100 values are used in
equation(6-4)to estimate 100 values for "b". Having generated a vector
of values for 3k associated with a vector of values for "b". the
computer performs the look-up procedure. The values for "b" from the
two distributions bounding the point of indifference as estimated in
the choice sequence discussed above. are entered. The computer then
searches for the two values of "b" out of the 100 calculated that most
closely approximate the entered values. The As associated with these

two "bs" become the estimates of the buyer's risk aversion coefficient.

117

Avsl
Ast

AvsJ

AvsC

Ava!

Avsl.

Avsl

Ast
AvsC
b Avsll

AvsD

Asz

AvsH

AvsP

Figure 6.5: Choice Tree for Interval Approach to Risk Aversion
Coefficient Estimation.

The third portion of the program estimates the premium the
farmer should be willing to pay. assuming the theoretical models are
correctly specified and the parameters correctly measured. In fact.
three different premiums are estimated in this part of the program.
high and low estimates based upon the theoretical model and the premium
required for an actuarially fair program.

To obtain these estimates. the farmer is asked to indicate
the level of insurance he would like to purchase, 50. 60 or 75 percent
of his average revenue over the base period. If he is uncertain which
coverage level he would prefer, he is allowed to examine all three
levels. Based upon his coverage choice, the model parameters (u. Y1, Y2
and P) are calculated from the revenue histogram developed in the first

section of the program. The two estimates of the risk aversion

118

coefficient from part 2 of the program are combined with these
properties of the farmer's PDF over revenue to calculate the loading
factor and the insurance premium. The actuarially fair premium is
calculated directly from the farmer's PDF over revenue.

The farmer is then asked which of the three premium
estimates he would be prepared to pay in exchange for the level of
protection offered by the revenue insurance policy. The premiums are
offered to the farmer in descending order of magnitude. For example.
if the loading factor is greater than 1. the highest premium estimate
will come from the theoretical model using the higher value for risk
aversion coefficient. The next highest premium will be the theoretical
estimate using the low risk aversion estimate and the least expensive
estimate will be the actuarially fair price. If the farmer is
unwilling to pay any of these amounts. he is asked to indicate the
maximum he would consider paying.

The respondents were told that in exchange for the premium,
they would be assured of a minimum return of so many dollars per acre
in the coming crop year. that they could expect to receive an indemnity
of so many dollars from the policy and that, on average, they would
make a claim on the policy one year out of X. Suppose. for example.
the farmer in question has annual gross receipts that average $100,000,
he opts for 75% coverage. the probability in the insured tail is .20
and the average outcome over the insured portion of the PDF is
$10,000. In exchange for a premium. this farmer would be assured that
his gross receipts in the coming year would be at least $75,000. On
average this policy will pay out $5,000 in benefits and a claim will be

made on it one year out of five.3

119

The Sample

A total of sixty farms from two areas of Michigan, the
"Thumb" and the south-central regions, were randomly selected from
Cooperative Extension Service census lists as participants in the
study. Of the sixty selected. nine were deemed to be inappropriate
subjects. sixteen were unavailable and fifteen refused to cooperate.
Furthermore. of the twenty who did participate. four had to be excluded
for a technical reason. to be discussed shortly. and one because the
data obtained were clearly inaccurate. The final sample was.
therefore. fifteen farmers. Table 6.2 summarizes some of the
characteristics of the 20 farms visited. The average size of the farms
included in the final sample of 15 was probably smaller than the
average commercial farm in Michigan. The size of the five farms
excluded were larger than the sample average. Gross receipts per acre
averaged $201.09 for the farmers included in the final sample. A wide
variation in gross returns per acre was also observed (from $48.05 to
$439.43 per acre). While data were not collected on the age of the
operator, the researcher's qualitative opinion is that the average age
of the operators in the final sample was above the average for farmers
as a whole. For example, the sample contained 4 farmers who were
"semi-retired". The sample included two dairy operations. a swine
operation. a cattle rancher and eleven cash-crop farms of various

types, mainly corn. dry beans, and wheat.

120

Table 6.2: Summary Description of Farms Visited

 

 

 

 

 

 

 

 

 

Farm Acres Average Ave. Gross
Worked Gross Receipts
Receipts Per Acre
Farms in Final Sample
1 120 $20,945.00 $174.54
2 1200 $293,168.00 $244.31
3 490 $50,001.30 $102.04
4 500 $98,903.00 $197.81
5 360 $136,403.00 $378.90
6 360 $100,007.00 $277.80
7 260 $62,824.10 $241.63
8 233 $11,196.70 $48.05
9 402 $62,445.30 $155.34
10 700 $163,120.00 $233.03
11 176 $41,565.00 $236.16
12 220 $44,070.90 $200.32
13 1200 $259,907.00 $216.59
14 76 $11,584.30 $152.43
15 31 $4.801.04 $157.41
ean Final Sample 422 $90.729.44 $201.09
Excluded Farms
1 780 $342,756.00 $439.43
2 450 $118.355.00 $263.01
3 280 $58.699.00 $209.64
4 1300 $369,771.00 $284.44
5 500 $214,279.00 $428.56
Mean Excluded Farms 662 $220,772.00 $325.02
Overall Mean 482 $123,240.08 $232.07

 

The Data

For the twenty farms that participated. average annual gross

receipts
farmer.

farmer's
were available.

There are

Total gross

tax records,

receipts,

for as many of the years from 1974 to

several

reported on schedule

were used as the base period.

reasons why tax data might

from farming were estimated from tax data supplied by

F of

be

 

121

unsatisfactory for the purpose at hand. The most important problem is

that farmers are allowed to use cash, as opposed to accrual, accounting

in estimating taxable income. Therefore. these records do not
necessarily measure receipts from a single crop cycle. There are two
important components to this argument. First. farmers can. and

regularly do move revenue and income between tax years by timing
purchase and sales decisions. Thus, the tax record is likely to
understate the variability of a farmer's revenue record. Second, since
tax records do not include the value of inventory adjustments within a
tax year, receipts reported for tax purposes may contain revenue earned
from several different crop cycles. A third problem with using tax
records are that they are sensitive records which some farmers are
reluctant to show to others. These are some of the obvious
shortcomings that must be accepted if tax records are used for the
purposes discussed. The overwhelming advantage of using tax records
for estimating costs and benefits of a revenue insurance program is
their availability. Most farmers do have a relatively comprehensive
record of tax receipts (if they are willing to share them). On the
other hand. many farmers simply do not have records on sales from a
given crop cycle and, by implication. changes in inventories.

As noted in Chapter 4, the risk aversion coefficient should
not be estimated over gross receipts since ones attitudes toward risk
are less likely to be determined by the total number of dollars flowing
through ones pockets than by the number that stick there. A preferable
variable over which to measure risk aversion would be a comprehensive
measure of wealth such as end—of—period owner's equity. Unfortunately,

many farmers do not have data on their end—of—period owner's equity and

122

fewer still have such records covering a ten year period. It was,
therefore. deemed necessary to proceed using annual income from all
sources to measure risk attitudes. These data were also obtained from
the participant's tax receipts.

Four farms were excluded from the final sample for what was
termed a technical reason. The reason for their exclusion was that the
maximum insurable level, 75 percent of the mean. was less than the
minimum level of gross receipts experienced by the farmer over the base
period. This being the case, the term (aPP - Y1) vanishes from the
premium calculation, meaning that the buyer should be unwilling to pay
anything for the insurance coverage offered. The implication is that
the farmer has found alternative ways of stabilizing his revenue and.
therefore, the insurance coverage has no value to him. This also means
that the pool of participants for a revenue insurance program is
unlikely to include the entire farm population.

There is an additional implication to be drawn from the four
exclusions. In Table 6.2, note that the mean revenue of the excluded
farms exceeds that of the 15 farms included in the sample. Since they
were excluded because their variances were small relative to their
mean, this contradicts the assumption underlying the aggregate models
of Chapter 5. Specifically, the aggregate model assumed that the mean
and variance of individuals in the pool could be described as stretched
or contracted versions of some standard PDF. This means that in order
to obtain a higher mean, a relatively greater degree of variance would
have to be accepted. For at least four of the individuals in the
sample, higher means were achieved without a large increase in

variance.

123

Results

The first question to be examined empirically is how well
does the model predict willingness to pay for insurance coverage? If
it does successfully predict willingness to pay, what conclusions can
be drawn about the potential cost of the program? Specifically, if the
price of coverage is sufficiently low, a high participation rate can be
ensured but the cost of the program to the government will be high. A
question of interest is. therefore, the loading factor that farmers
would be willing to pay for revenue insurance coverage. since this will
determine the amount above indemnity costs that farmers might willingly
pay. If farmers are willing to pay a premium that is greater than an
actuarially fair one, then some of the administrative costs of the
program would be covered by their premiums. Yet another issue is the
effect of an increase in the variability of outcomes on the cost of
insurance. ‘

At a more aggregate level there is the question of the
justifiability of the simplifying assumptions made concerning the PDFs
of the clients in an insurance pool? The shape of the aggregate demand
curve is also of concern. Aggregate demand will be derived by
exploring the relationship between participation rates and the loading
factor. Finally, the data can be used to examine the effect of
different subsidy rates on the cost of supplying revenue insurance.

Table 6.3 summarizes some of the results of the model trials
with respect to farmer willingness to pay for insurance coverage. The
results discussed are for coverage at 75 percent of the mean. Few data

were available for coverage at the 50 and 60 percent levels. Many

124

farmers inquired about these levels of insurance but few had
experienced revenue levels below the 50 and 60 percent levels during
the base period and were. therefore. excluded for the technical reason
discussed above. It was felt that the small numbers of respondents
who did qualify, could not give a very useful picture of demand for
insurance at these levels. As noted at the outset. the actual field
trials were conducted using a different model. The column headed
original maximum bid price lists the maximum bid price offered by the
farmer in the field tests. The third and fourth columns list the high
and low bid price estimates of the revised model. In the best case.
the new estimates would have bounded the old maximum bid price. Only
two of the predictions did bound the old bid price. However, the low
and high average premiums do bound the average maximum bid price from
the original model. It is also very encouraging that in only three
of the fifteen cases did the model fail to produce a premium that the
farmer would be willing to pay. This is shown by comparing the
original bid price with the bid price predicted by the revised model.
If any of the revised model predictions are less than the original bid
price. it is assumed that the farmer would pay this amount. Therefore,
only the 6th, 7th and 9th farmers would not have found a premium they
would have paid under the revised model. Finally, the fact that
premiums predicted by the model are. with few exceptions. of a
believable magnitude is also encouraging.

The average annual indemnity received by each farmer is
listed in the fifth column of Table 6.3 and the probability of
obtaining an indemnity is listed in the sixth column. The final column

lists the estimated risk aversion coefficient for each farmer. A

125

positive (negative) value of implies risk averse (loving) attitudes.

 

 

 

 

 

 

TABLE 6.3: Model Performance and Insurance Characteristics of the 15
Farms Studied, for 75 percent Coverage.
Farmer Original High Low Ave. Indemnity Probab. Lambda]
Bid Price Estimate Estimate Received/Acre Indemnity
Per Acre Per Acre Per Acre
1 1.90 .86 .73 .42 .1114 .00020
2 6.32 .41 —3.12 2.02 .1031 .00002
3 4.99 .32 -2.91 1.88 .1119 .00003
4 9.07 12.51 6.93 2.16 .1286 .00030
5 6.91 9.94 3.89 6.91 .2697 .00001
6 1.86 27.29 20.94 7.36 .4219 .00013
7 .77 24.93 17.81 2.69 .1806 .00027
8 13.13 2.44 2.01 2.01 .3002 .00007
9 5.00 11.28 6.16 1.50 .1162 .00040
10 2.64 2.54 1.51 .64 .1320 .00007
11 3.77 1.69 1.41 .79 .0710 .00011
12 6.03 3.10 2.33 1.53 .1603 .00009
13 4.49 -.19 -4.48 1.33 .1341 .00002
14 2.47 1.11 .54 .01 .0164 .00011
15 10.00 8.89 6.66 7.68 .3549 .00011
verage 5.29 7.14 4.03 2.60 .1742 .00012
Etandard Deviation (.1123)
The high estimate of the revised model provided per acre

premium estimates of a reasonable size and in the area of the maximum

bid price voiced by the buyer for most cases. However, several of the

estimates were not at all close to the original value. In particular

when an individual indicates he is risk preferring in the second

portion of the computer simulation. the estimates for the maximum bid

price tend to bear little resemblance to the maximum bid price

expressed by the farmer. This highlights several points. First. we

would not expect to find farmers who are risk preferring. Being a
lover of risks implies a propensity to go against the odds. In the
long run, going against the odds will always be a losing proposition.

If a farmer was truly risk preferring he would eventually go out of

126

business as the odds catch up with him. It is, of course, possible to
exhibit risk preferring behavior in a given instance. This is borne
out by the discussion of Ehrlich and Becker as well as Robison and Lev
(1984). But, we would not expect to see risk preferring behavior
consistently and and in the long run.

Second, the seeming inability of the model to perform well
for ostensibly risk preferring buyers indicates that care must be taken
in the implementation and interpretation of models of this sort.
Clearly the results of the model are extremely sensitive to the risk
aversion coefficient. The derivation of this parameter is not without
pitfalls. Beyond the theoretical questions surrounding the interval
approach using hypothetical values, there are a number of
implementation issues of tremendous importance. Experience with
implementation indicates that the process is difficult to explain in a
way that is clear to the farmer without introducing the possibility of
interviewer bias. There is. in addition, the problem of type 1 versus
type 2 error discussed above.

The discrepancies noted for farmers 6 and 7 point out, I
believe. the importance of data quality and quantity for the successful
use of this model. In both cases the farms had undergone extensive
reorganization in the recent past. It was felt that the revenue record
of the farm prior to reorganization would not provide an accurate
picture of the revenue experience of the farms as currently operated.
Thus, both farms had considerably less than the ten years of data
sought for the base period. In addition. each of these farmers
indicated relatively strong risk aversion. Relatively unstable

earnings (caused at least in part by the limited length of data series)

127

and high risk aversion combined to increase dramatically the estimated
bid price for these two farmers.

The results from farmers 6 and 7 are particularly
instructive because these were both relatively young farmers. Their
situations reflect several questions which must be addressed by any
revenue insurance program that is implemented. First. since these two
farmers had been on their own for a relatively short period of time
they did not have a lengthy revenue record. Much as the young driver
pays relatively high insurance prices to insure his vehicle because he
is unable to prove he is the exception to the rule. a safe and prudent
teenage driver, young farmers will face a similar problem when signing
up for revenue insurance. The solution to this problem in the crop
insurance program has been the liberal use of county data to supplement
(replace) own-farm data. For the reasons discussed in Chapter 2, this
is not a wholly adequate solution.

These cases raise the larger question of how the insurance
program will handle policies for farms that undergo major changes in
organization: the break-up of a partnership, a substantial change in
farm size, a change in the types of crops or livestock produced and so
on. This presents the policy maker with a dilemma. Farm
reorganizations are often a very necessary action and it seems
unfortunate that young farmers are penalized simply because they
haven't been in farming for very long. However, the policy maker does
not want to reduce the amount of information conveyed by the insurance
premium regarding market conditions. Specifically, a lower premium is
the reward for management decisions that. in the view of the insurance

company, are prudent; ones that reduce the variability of earnings.

128

The issue is, therefore, how a revenue insurance program can be
structured so that it doesn't unduly punish young farmers and farmers
who alter the organization of their operation yet retains the ability
to convey market information.

In Chapter 4 the possibility that young farmers might have a
greater propensity to purchase revenue insurance was discussed. The
relatively large risk aversion coefficient of farmers 6 and 7 may be
indicative of this greater propensity. As discussed in Chapter 4.
since young farmers are less likely to have built up much equity in
their farm and will have a smaller credit reserve, they will probably
be more sensitive to down-side risks. This could easily explain an
unusually high propensity to purchase revenue insurance amongst young
farmers. This propensity may, however. be outweighed by the need to
control cash expenses and the relatively higher prices demanded by
insurance companies to cover their risks. For this sample. the desire
to control down—side risks seems to have been of greater relative
importance.

One of the more surprising aspects of Table 6.3 is the
relatively low cost of revenue insurance in terms of benefits paid out
per acre. Not only is the overall average indemnity under $3.00 per
acre per year, but none of the individual average indemnities exceeds
$8.00 per acre per year. The low indemnities are probably the result
of several factors, two of which may be of transcendent importance.
First, as noted in Chapter 2. the expected negative correlation between
price and quantity should make the revenue PDF more stable than either
the price or quantity PDFs individually. Second. the use of tax data

could, for the reasons stated above, overstate the degree of stability

129

of revenue. Additional factors explaining the observed stability might
be model misspecification, an insufficiently long base period or an
unrepresentative sample.

Finally, the distribution of the cumulative probabilities
listed in the sixth column of Table 6.3 is quite remarkable. In the
model of aggregate supply developed in Chapter 5, the hypothesis was
that the probability in the insured tail of each buyer's PDF was the
same but that the distribution of that probability was stretched or
contracted by the factor a. In eleven of the fifteen cases listed in
Table 6.3 the probability in the insured portion of the PDF is within
plus or minus one standard deviation of the average of .1742. In
contrast to the implication drawn from the exclusion of the four
farmers who had high mean-low variance outcomes. this phenomenon
supports the assumption employed. In the aggregate more than 50
percent of the farms in the sample seem to be quite adequately

described by the simplifying assumptions.

130

Aggregate Results

 

The aggregate models use the assumption that the PDF of each
buyer in the market can be described as a modified version of some
standard PDF. In the empirical test of the aggregate model the
numeraire distribution was assumed to be the average PDF. That is. it
is assumed that an individual's PDF can be approximated by multiplying
the mean. Y1. and Y2 for the insurance pool by the appropriate shift
factor, a. In Table 6.4 the mean return for the fifteen farm sample is
given as $93,159.31, Y1 as $10.887.80, and Y2 as $82,271.51. The

loading factor and premium for buyer 1 are, therefore. defined as:
v a l - x a (.75(93159.31(1 - .173) - 82271.51)
i i i
B

= 1 - A a (-24279.84)
i i

and

u,
11

I i i

3 V a (990.01) v
i i

where

a = (P*/93159.31)
i i

Table 6.4 lists the £1 for each buyer and compares the
loading factor and premium/acre generated by the model developed in
Chapter 4 to the loading factor and premium generated when the
simplifying assumptions of Chapter 5 are employed. The loading factors
listed as coming from the Chapter 4 model use the high estimate for the
risk aversion coefficient. Likewise, the premiums in the next to last

column use the high estimate for .k.

131

There is a remarkably good fit between the values for the
loading factor calculated in the two different ways. While the
differences between individual premium estimates are substantially
greater than those observed for the loading factor. the difference
between overall average premium estimates is also extremely small.

Table 6.4: Comparison of Measured and Estimated Values for
the Loading Factor and Premium.

 

 

 

 

 

 

Chapter Chapter Chapter 4 Chapter 5
Farmer Mean 4 Loading 5 Loading Premium Premium
Revenue Alpha Factor Factor Estimate(a) Estimate(a)
1 20945.00 .22 2.04 2.09 103.49 600.88
2 136403.00 1.46 .20 .17 148.86 323.41
3 100007.00 1.07 .21 .18 144.60 250.54
4 62824.00 .67 5.80 5.89 3251.68 5018.76
5 293168.00 3.15 1.44 1.39 11923.10 5584.66
6 66668.00 .72 3.71 3.36 13372.90 3073.85
7 118685.00 1.27 9.26 9.33 12465.40 15206.64
8 11196.70 .12 1.21 1.19 567.38 183.35
9 62445.00 .67 7.51 7.62 4534.25 6537.56
10 163120.00 1.75 3.95 4.05 1778.28 9086.00
11 41565.00 .45 2.15 2.19 297.49 1253.54
12 44071.00 .47 2.02 2.05 681.66 1238.82
13 259907.00 2.79 -.14 -.17 ~226.09 -590.25
14 11584.00 .12 1.32 1.34 83.99 212.63
15 4801.00 .05 1.16 1.14 271.21 75.14
Average 93159.31 1.00 2.79 2.79 3293.21 3203.70
Y 2 10887.80
1
Y = 82271.51
2
(a) Annual premium.
Several interesting patterns emerge from Table 6.4. First.

at least in the aggregate, the simplifying assumptions employed in
Chapter 5 provide an accurate picture of the insurance market. The
fact that the cumulative probability contained in the insured portion

of many of the buyer's PDFs is quite similar and the extremely good

132

estimates of the loading factor obtained when the simplifying
assumptions are employed, leads to the conclusion that the lower
reaches of the PDFs of our fifteen farmers are fairly similar. The
fact that the premium estimates differ by considerably greater amounts
indicates that there are greater differences in the PDFs of the sample
farmers over the uninsured portion of their PDFs. A much larger and
more broadly drawn sample is required before much can be made of the
patterns detected in the 15 sample farms. What can be said is that for
this sample the differences between the loading factors and premiums
calculated by the two methods are not significantly different from
zero. The hypothesis that they are different from each other is tested
4

and rejected in Table 6.5.

Table 6.5: Test the Significance of Differences in the Loading
Factor and Premium Estimates Using Two Estimation

 

 

 

 

Techniques.

Loading Loading Diff. Diff. Premium Premium Diff. Diff.

Factor Factor From Mean Chapter Chapter From Mean

Chap.4 Chap.5 Squared 4 5 Squared
2.04 2.09 -.05 .0025 103.49 600.88 -497.39 247396.81

.20 .17 .03 .0009 148.86 323.41 -174.55 30467.70
.21 .18 .03 .0009 144.60 250.54 -105.94 11223.28

5.80 5.89 —.09 .0081 3251.68 5018.76 —1767.08 3122571.73
1.44 1.39 .05 .0025 .11923.10 5584.66 6338.44 40175821.63
3.71 3.36 .35 .1225 13372.90 3073.85 10299.05 106070430.90
9.26 9.33 -.07 .0049 12465.40 15206.64 —2741.24 7514396.74
1.21 1.19 .02 .0004 567.38 183.35 384.03 147479.04
7.51 7.62 -.11 .0121 4534.25 6537.56 -2003.31 4013250.96
3.95 4.05 -.1 .0100 1778.28 9086.00 -7307.72 53402771.60
2.15 2.19 -.04 .0016 297.49 1253.54 -956.05 914031.60
2.02 2.05 —.03 .0009 681.66 1238.82 -557.16 310427.27
-.14 -.17 .03 .0009 -226.09 -590.25 364.16 132612.51
1.32 1.34 -.02 .0004 83.99 212.63 ~128.64 16548.25
1.16 1.14 .02 .0004 271.21 75.14 196.07 38443.44
2.79 2.79 .0013 3293.21 3203.70 89.51

SUM OF ERRORS SQUARED .1690 216147873.46

STANDARD ERROR .1099 3929.27

T-COEFFICIENT .0458 .0882

 

 

133

The Effect of Increased Instability on Premium Costs

One of the shortcomings of using tax data is that the
stability of a farmer's revenue experience is likely to be overstated.
A simple, and somewhat imperfect, way of examining the sensitivity of
the model to increases in instability is to increase the value of a'.
Increasing c1, ceteris paribus. is an imperfect test because this
increases the mean as well as the variance of outcomes. To generate
the numbers in Table 6.6. the alpha value for each farmer was doubled.
The original estimates for the loading factor and premium (employing
the original value foriI) are repeated from Table 6.4 in the final two
columns of Table 6.6.

Perhaps the most interesting feature of Table 6.6 is that
doubling a increases the average premium by more than a factor of
three. The implication is that the premiums might increase
substantially with an increase in the variability of outcomes. The
increase in the premium predicted by the model is not constant across
farms. however. The most obvious examples of this are farmers 2 and 3.
An increase in a for these two farmers would. according to the model.
cause both farmers to reduce the amount they would pay for insurance by
a substantial amount. In fact the loading factor for these two
purchasers changes sign with the doubling of alpha.

The other outstanding feature of Table 6.6 is the extreme
values predicted for some of the premiums. Quite clearly no one is
going to pay over $115/acre to obtain the protection offered by revenue
insurance. This extreme value is explained in part by the limited
number of years included in the base period of farmer 7 and partly by

the assumption that the risk aversion coefficient for the farmer

134

remains constant despite the fact that we have increased his expected

revenue level relative to the first case.

Table 6.6: Comparison of Measured and Estimated Values for
the Loading Factor and Premium When Alpha Doubles

 

 

 

 

 

New Loading New New Old Loading Old
Farmer Alpha Factor Premium Cost/ Factor Premium
Estimate Estimate Acre Estimate Estimate
1 .45 3.18 $1828.03 $15.23 2.09 $600.88
2 2.93 -.65 -$2454.23 —$6.82 .17 $323.41
3 2.15 —.64 -$1745.67 -$4.85 .18 $250.54
4 1.35 10.78 $18600.86 $71.54 5.89 $5018.76
5 6.29 1.77 $14283.44 $11.90 1.39 $5584.66
6 1.43 5.71 $10463.61 $21.35 3.36 $3073.85
7 2.55 17.65 $57565.52 $115.13 9.33 $15206.64
8 .24 1.38 $425.75 $1.83 1.19 $183.35
9 1.34 14.24 $24434.48 $60.78 7.62 $6537.56
10 3.50 7.11 $31862.06 $45.52 4.05 $9086.00
11 .89 3.39 $3871.31 $21.99 2.19 $1253.54
12 .95 3.09 $3744.35 $17.02 2.05 $1238.82
13 5.58 —1.33 -$9502.30 -$7.92 -.17 -$590.25
14 .25 1.67 $532.22 $7.00 1.34 $212.63
15 .10 1.28 $168.66 $5.53 1.14 $75.14
Average 4.58 $10271.87 $25.02 2.79 $3203.70

The Aggregate Demand Curve

The aggregate demand curve for the fifteen farms is in terms
of the loading factor charged and the number of farmers participating.
One reason for interest in the aggregate demand curve is to be able to
answer the question: 'If the government is going to use a single
loading factor to calculate the premium. what should it be?’ Put
another way, if the government wanted to achieve some level of
participation in the program. 75 percent of all full time farmers for

instance. what is the maximum loading factor it could charge? Figure

135

6.6 shows the relationship between the loading factor and
participation. As we would expect, greater participation is achieved

as the loading factor is lowered.

Loading Factor

15d

 

Number of Participants

5 10 15 20

Figure 6.6: Participation as a Function of the Loading Factor

The relationship between the gross receipts the government
could expect to receive and the loading factor is plotted in Figure
6.7. Gross receipts increase as the loading factor increases until it
reaches 4.00. at which point they begin to fall. It is interesting to
note that only slightly more than one in four farmers would be expected
to participate if the loading factor was 4.00. This implies that there
is probably a positive relationship between expense to the government

and levels of participation.

136

Returns

520.000-

510.000-

 

Loading Factor

 

Figure 6.7: Expected Returns in a Revenue Insurance Program for
Different Loading Factors.

Table 6.7 summarizes the relationships between the loading
factor, the participation percentage, revenue for the seller and the
surplus that would be available to the seller to offset non-indemnity
costs.

Table 6.7: Participation Rates, Seller's Returns and Seller's Surplus
as Related to the Loading Factor

 

 

Loading Percent Average Seller's Seller's

Factor Participation Indemnities Returns Surplus

9.00 6.7 1630.52 14674.65 13044.13
7.00 16.7 2488.40 17418.78 14930.38
5.00 20.0 3351.49 16757.43 13405.94
4.00 26.7 5592.46 22369.83 16777.37
3.00 33.3 6508.36 19525.07 13016.71
2.00 53.3 7972.60 15945.17 7972.57
1.25 66.7 12159.34 15199.16 3039.82
1.00 80.0 12379.10 12379.10 0.00

 

 

 

137

In the analysis to follow. it is assumed that the loading
factors calculated from the aggregate model and reported in Table 6.4
are accurate. Thus. if farmer 1 has an optimal loading factor of 2.09,
this is taken to be an accurate measure of his willingness to pay for
revenue insurance protection. It is also assumed, quite reasonably,
that if he would pay a premium based on a loading factor of 2.09, he
would be willing to pay one based on a loading factor of 2.00. Use of
a smaller loading factor simply means he will get the same level of
coverage at a lower price.

Now, suppose the government wanted to assure that two-thirds
of the farmers in the sample will participate in a revenue insurance
program. Based on the results reported in Table 6.7, the government
could charge a flat loading factor of 1.25 and obtain the desired level
of participation. This means that the government could expect to be
able to use roughly twenty-five percent of the premiums collected to
off-set the cost of administering the program. For example, based on
Table 6.4, if the government used a loading factor of 1.25 we would
expect farmers 1, 4. 5, 6, 7, 9, 10, 11, 12. and 14 to participate in
the program. Based on the figures in Table 6.7, the government could
expect to earn $15199.16 from these ten farms and have over $3000.00 to
use for operating expenses. If the approximate cost of administering a
revenue insurance program was known, an estimate of the drain this type
of program would make on the federal budget could be made.

Insuring a given percentage of the land in agricultural
production may be of greater interest than insuring a given percentage
of the farming population. Table 6.8 examines the trade—off between

the loading factor and the proportion of acreage insured. Comparing

138

Tables 6.7 and 6.8, we see that there is relatively little difference
between participation rates as a function of the loading factor when
measured on a participant or an acreage basis. One extremely important
and interesting implication of this relationship, if it holds in the
broader farm population, is that a revenue insurance program structured
like the one analyzed in this thesis may be equally effective in

attracting participants from small and large farms.

Table 6.8: The Proportion of Acreage Covered at Various Loading Factor

 

Levels.

LOADING PERCENT ACRES

FACTOR IN PROGRAM_
9.00 7.9
7.00 14.3
5.00 18.4
4.00 29.4
3.00 37.2
2.00 45.3
1.25 65.5
1.00 69.7

In summary, the models as formulated in this dissertation
have performed remarkably well, at least on the admittedly small sample
considered. In addition to the support lent to the theoretical models,
the case studies have provided several valuable insights into the
problems and potential of a revenue insurance program.

Qgglitative Assessment

In addition to the numerical data collected from farmers.
their subjective opinions about a revenue insurance program were
sought. Several things about their responses were noteworthy. First.
the fact that one-quarter of the farmers contacted refused to cooperate
is indicative of a degree of disinterest in the subject in the farming

community. Second, of the farmers who did participate in the study,

139

the majority voiced a great deal of skepticism about the program. Many
felt that it would be too easily manipulated by unscrupulous farmers.
The opinion that the record keeping requirements would be more trouble
than the program would be worth was also a common response. Others
indicated a deep-seated suspicion of insurance companies, feeling that
however the program was structured, they would be the loser. However,
despite these rather negative reactions, virtually all indicated an
interest in the program if the protection discussed was available at

the prices indicated by this model.

Summar

The empirical work described in this chapter is the first
effort to guage the cost of and farmer attitudes toward the proposed
revenue insurance program. Many farmers indicated a lack of interest
in the program by choosing not to participate in the study. In
addition, those who did participate voiced a great deal of skepticism
about the workability of the program. Despite this scepticism
virtually all of the farmers in the sample voiced an interest in
obtaining this type of protection.

The empirical data lend qualified support to the theoretical
models constructed in Chapters 4 and 5. Before the strength of that
support can be assessed. a much broader sample of farms will have to be
surveyed. Based on the current sample, it appears that a revenue
insurance program might be much less expensive to operate, in terms of
indemnity payments, than expected. The evidence suggests farmers
would, on average. be willing to pay somewhat more than an actuarially
fair price for insurance of this type. This has important policy

implications since it indicates that at least a portion of the

140

administrative costs of the program could be off-set by farmers'
premiums. A major qualifier to this assessment is that the data used
could have a bias in favor of stability. If the data exaggerate the
stability of farm revenue, the cost per acre of the program could
increase dramatically and the willingness to pay a loading factor
greater than one could fall. Finally. a revenue insurance program
appears to have a similar degree of appeal across sizes of farms
meaning, for instance, that participants in the program are likely to
be drawn from all sizes of farms indicating that the effect of the
program may be scale neutral.

The results of this survey should be interpreted as quite
encouraging for those interested in a revenue insurance program. They
indicate that there is a degree of resistance to the idea of revenue
insurance in the farming community but that this skepticism can be
overcome by a program offering protection at a price slightly greater
than required for actuarial soundness.

Having completed the theoretical and empirical treatments of
the revenue insurance option, it is time to step back and try to gain a
broader perspective on the topic. The next chapter provides this

perspective.

141

The minimum value for Plan C is midway between the minimums for
Plans A and B. The range of Plan C is, like Plan A, one-half the
range of Plan B. Thus to derive the maximum for Plan C. we add
(125,000/2) to 40,625.

. This formula was developed by Dr. Lee Sonneborn of the mathematics

department at Michigan State University. Dr. Sonneborn's assistance
is greatly appreciated.

. The insured level. an. is:

.75(100000) = 375.000.00

The average indemnity, an? - Y . is:
1

.75(1000OO(.2)) - 10000 = $5.000
The years to payout, 1/P, is:

1/.2 = 5 years

. The t-statistic is derived from the following formula:

t = (i - M/(smfi)
Where
2 — P = Mean of the difference between the Chapter 4 and 5
estimates.
3 = Standard error of the estimate.
n a Sample size.

Chapter 7

Revenue Insurance in American Farm Policy

This chapter examine the likely impact of a revenue
insurance program on two farm problems: low or variable farm incomes

and unstable agricultural commodity markets.

Egggglncome Problems ang Revenue Insurance

Since the Great Depression, the U.S. has had a variety of
public programs that have intervened in agricultural markets. At their
inception. and for much of the time since, there was at least tacit
agreement amongst most policy makers that the issue to be addressed by
farm programs was the wide difference between the income levels of farm
and non-farm households. There were many hypotheses put forward
purporting to explain the problem of low incomes in agriculture:
excessive amounts of labor or other inputs that were "stuck" in
agriculture, outward shifts of the supply .curve induced by
technological change coupled with an inelastic and stable demand curve.
the structure of agriculture vis-a-vis other sectors of the economy
(competitive versus monopolistic or oligopolistic markets) to cite a
few. Others argued that the problem was overstated because of a
statistical illusion (farmers were better off than statistics implied
because of home consumption of production. farm-supplied inputs, asset
appreciation, etc.).

In the 1970s the average income of farm families approached,

142

143

then exceeded, that of non-farm families. Increasingly. the farm
problem was being defined by commentators as something other than low
income levels. Concern has shifted to the variability of farm incomes
rather than the absolute or relative level. This term used to describe
this concern with variability is "cash flow". There are two
aspects to the cash flow problem faced by farmers. One is the fact
that a major portion of a farmer's returns has typically been in the
form of a capital gain on his land. This return is realized only when
the land is sold. Expenses, on the other hand. do not wait until the
farmer sells his land. Thus. there is a divergence between the timing
of income flows and cash expenses. A second aspect of the problem is
the variability of earnings. A farmer has a large component of fixed
costs which must be met if he is to retain his land. He also has
variable costs that are incurred several months before he realizes a
return. Furthermore, the level of his return is uncertain at the time
expenses are incurred. In summary, cash flow problems develop
because returns are variable and clustered near the end of the stream
of returns while expenses are relatively evenly spaced throughout the
period of land ownership.

In the early 19803 we have, however, seen a precipitous drop
in farm income. The Detroit Free Press reported that farm incomes in
Michigan would be 50 percent lower in 1981 than they were in 1980. The
same source reported that 52 percent of Michigan farmers with loans
from the Farmers Home Administration were delinquent in their loan
payments in 1983.1 It is an open debate whether low or variable
incomes is the dominant issue. The question of concern here is the

effect of revenue insurance on these farm income issues.

144

In Chapter 4 it was shown that revenue insurance would be
expected to reduce the mean and variance of the revenue PDF. Under the
assumptions employed in the model, this also means a fall in the mean
and variance of farm incomes. Any other result would be implausible.
If income increased when insurance was purchased, there would be no
limit to a buyer's demand for insurance. An increase in a buyer's
income also means the insurance company is disbursing more than it is
collecting and this could not continue indefinitely without the seller
going bankrupt. The conclusion is, therefore, that a revenue insurance
program, if run on actuarial principles, is an ineffective and
inappropriate means of increasing income levels within the farm
papulation. On the other hand. revenue insurance is expected to reduce
the variability of revenue.

Entry barriers are an important problem in American
agriculture which are affected by cash flow problems. The major
barrier to entry in the farm sector is the extremely high cost of
starting up. In particular, many authors have discussed the problems
arising from very high land prices. Raup found that between 1967 and
1977, agricultural land prices went up 100 percent with 80 percent of
the increase occurring between 1972 and 1977. Land prices increased
more in the Corn Belt, Northern Plains and mid-Atlantic states than
elsewhere in the U.S.

Melichar shows that current and past land prices may be
justified in terms of the total returns to that factor. However, these
high prices are likely to lead to cash flow problems, large increases
in debt, troubles for beginning farmers and an influx of wealthy

investors from outside farming who. for a variety of reasons. are

145

interested in acquiring farmland. Robison and Brake show that during
inflationary periods, cash flow problems will exist when purchasing a
nondepreciating asset, such as land, even if inflation is perfectly
anticipated, if the debt has to be paid back in equal installments.
The result is, as Robison and Brake say, with 100 percent financing.
"outside incggg_(their emphasis) equal to the first period's capital
gain will be required to service the debt in the first year if only
interest cost is repaid."2 If beginning farmers have little or no
outside income, this can be a formidable problem. According to Carter
and Johnson capital gains as a percentage of farm production income
increased from 20 percent in 1960 to 175 percent in 1975.

Lee and Rask and Harris and Nehring have constructed models
to examine the bidding process for land in agriculture. Lee and Rask
compared the maximum bid price for land in the Corn Belt under a
variety of conditions. They found that regardless of the scenario.
those buying whole farms of an economic size (ie. wealthy investors)
and those adding to existing farms that were already of an economically
viable size, could outbid new entrants and owners of small to moderate
sized farms. Harris and Nehring examined the characteristics of buyers
who could afford to make higher bid prices and concluded that no single
investor is likely to match all criteria. However, safe assumptions
(such as decreasing risk aversion over wealth and lower time preference
rates for wealthy individuals) make it likely that wealthy investors
will generally make higher bids for a given plot of land. The
conclusion reached is that with high and rising land prices. beginning
farmers have a difficult time competing for land that comes onto the

market and. because of cash flow problems, have a difficult time

146

keeping land they do acquire.

Revenue insurance will reduce the variability of returns and
should, therefore, reduce the importance of this aspect of the cash
flow problem. Variability of returns is particularly troublesome for
young farmers. For example, if a young farmer has a poor revenue year
early in the period of land ownership when he has little owner's
equity, he may find it difficult to qualify for loans needed for his
economic survival. By increasing the minimum level and decreasing the
variability of returns, revenue insurance could reduce this problem for
young farmers.

In addition, in Chapter 6 it was noted that younger farmers
may have greater propensity to purchase revenue insurance. If this
finding holds for the farm population as a whole, the consequences of
this greater propensity to purchase revenue insurance could be
important. For one thing, it would decrease the cash flow problems of
this vulnerable group relative to the general farm population. In
addition, with assurance of some minimum level of annual gross
receipts, access to credit should be increased. Both of these results
would be expected to improve the ability of younger farmers to acquire
and hold land.

There are, however. two other factors that would be expected

to have the opposite effect. First, purchasing revenue insurance will
lower income. This would increase the need for off-farm sources of
income in the early years of farming to cover cash costs. Secondly.

stabilizing gross receipts in farming would increase the attractiveness
of investments in agricultural land. This would be expected to drive

bid prices even higher. As Harris says, "it is likely that any

147

governmental policy designed to enhance or stabilize farm income will
be inconsistent with our objective of stabilizing land prices."3

Further empirical work to quantify the degree to which young
farmers are more likely to purchase crop insurance is needed. However.
the results of the empirical work reported in Chapter 6 indicates that
the desire to reduce the risk of a low revenue year may be the dominant
factor in the revenue insurance purchase decision. It could be argued
that the lower income level caused by purchase of a revenue insurance
policy would be a price worth paying if this would significantly
improve the farmer's ability to retain control over his largest asset,
his land base. The historical record indicates that for whatever
reasons, farmers have been willing to pay this price since farm incomes
have tended to lag behind those of the non-farm population. The
purchase of revenue insurance may simply be a different manifestation
of this willingness. The impact of increased stability of returns on

bid prices for land is a dynamic question which the models constructed

are unable to address directly.

148

Instability in Agricultural Markets and Revenue Insurance

An issue closely related to low and variable incomes in
agriculture is the problem of instability in agricultural markets.
Instability in these markets affects the prices and quantities of
agricultural products. This instability affects not only the earnings
of farmers but other participants in the food system as well.

Few farm policy issues have received more attention than
instability in commodity markets. There is not much argument that
agricultural markets have been quite unstable. especially in the recent
past. As Grennes. Johnson and Thursby point out. the real price of
wheat trended downward almost continuously from 1946 through 1970. In
the early 19703, the price rose rapidly, reaching a post war peak in
the winter of 1973/74. By 1977 prices had fallen to nearly the lowest
price of the century, the 1932 price of $1.20 per bushel (real 1967
dollars). Harrington examines the variability of the index of prices
received for all agricultural products. for all crops, for all
livestock and various definitions of farm income. He calculates the
coefficient of variation (oz/u X 100) for these measures during three
periods: 1955-1963, 1964 - 1971 and 1972 - 1978. For virtually every
category the coefficient of variation increases monotonically as you

approach the most recent period. Figure 7.1 illustrates the percentage

WHEAT: EXPORT REVENUE A8 A
PERCENTAGE OF THE VALUE OF
PRODUCTION

 

 

reacts!

fl

ni- -

fli- .4

”- _,
d

~- 7

'0 l i l l i

 

 

 

1'11“ I.” 1.“ mo 1975 in
'3'.” 1‘13 (02” (‘75. (50'

 

W xfitmmuawus
mum-mummsmus

Figure 7.1:

149

CORN: EXPORT REVENUE A8 A
PERCENTAGE OF THE VALUE OF
PRODUCTION

PERCENT
J!

 

 

 

 

l L i l 1

 

D

I.“ 1”. 1m 1005 1.” 1m 1m
1“ 1..“ "1. "1. "D.”

w.w-W ‘——— “‘

'fl".m~~m.u

SOYIEANS: EXPORT REVENUE A8
A PERCENTAGE OF THE VALUE OF
PRODUCTION

fl

 

88883

 

 

 

l l l l i

10
I“! I“. in I“ 1070 1.75 I!”
(20.0 Mel 161.. (5121 ms
wammwmnamm
cum-mmnmsm

 

Export Revenue as a Percentage of the value of

Production for Wheat, Corn and Soybeans. 1951 - 1978(a)

a. Ronald L.
International

Meekhoff.
Markets". in

Structure

"Implications of Increased Reliance on
Issues of

American

Agriculture, U.S.D.A.. ESCS, Ag. Econ Rpt. 438. pp 258-259.

of the value of production earned by exports for wheat. corn and

soybeans for the period 1951 to 1978. The volatility of this

experience is evident. As exports have become a more important part of

farm sales. the variability of export earnings has had a greater

influence on the revenue experience of the farming sector.

Instability in agriculture has many dimensions that

recommend it as an issue for public policy. Many argue that there is a

direct relationship between instability and farm bankruptcies.

150

Bankruptcies cause both economic and psychic losses. It is not the
costless adjustment that economic theory would indicate. Lawyer's fees

and other transactions costs associated with the bankruptcy procedure

are incurred. There are also costs of moving, retraining and so on.
There is a loss of the farmer's agricultural talents. There are costs
borne by the farmer's creditors as well. Table 7.1. reproduced from

Kauffman's work, indicates one of the costs associated with the hog
cycle, unplanned refinancing of loans. The clear implication of Table
7.1 is that increasing leverage increases the likelihood of
refinancing. Refinancing would be expected to occur when the market for
hogs falls and would increase the lender's costs. There are, in
addition, the psychic costs of losing the farm and the lifestyle

associated with farming and with the need to adapt to a new occupation.

Table 7.1(a): Effect of Leverage on Refinancing (Percent)

More than 75% of Operating Capital Borrowed

 

 

 

I Yes I No I

I I I

I I I I

Refinancing I Yes I 56 I 44 I
Required I I | I
I I I

I 19 I 81 I

I

I

I No
I I I
(a)Source: Kauffman, 1983. page 141

 

Even if there is not a direct connection between instability
and bankruptcy, instability does call forth actions which entail
opportunity costs. Instability rewards protective actions that may or
may not be productive. For example, profitable investments may be

foregone so the farmer (and his bank) can maintain a large credit

151

reserve.

Furthermore, instability in agriculture produces secondary
effects. Rural communities and agricultural supply industries are
affected by changes in agricultural prosperity. For example. last

year's Payment in Kind program, which paid farmers in grain to take
their fields out of production, had a substantial impact on the
economic health of the farm implement and agricultural chemical
industries. Consumers are also affected by this instability, both
directly. via the prices paid at the supermarket. and indirectly, by
the effect on the cost of living allowance calculation used to index
many wage agreements.

Finally, agricultural stabilization programs may be seen as
attempts by the government to undo with its left hand what it has
caused with its right. Seen in this way. price supports, the farm
credit system, and other policies are counterweights to an overpriced
dollar, high real rates of interest, grain embargoes and so on. Thus.
if the government induces instability by some of its actions it is only
”fair" that they attempt to undo some of the effects of those actions.

The ability of revenue insurance to reduce instability in
agricultural markets depends upon the cause of the observed
variability. Potential sources of agricultural instability discussed
in the literature include the performance of the general economy.
foreign trade, agricultural policy, depletion of grain reserves.
misallocated resources. the industrialization of agriculture. the
environment. technological change, and the structure of the food
system. Some of these hypotheses will receive more extensive treatment

in the discussion to follow.

152

The Business Cycle

Researchers in agricultural economics who have examined the
importance of links between general macroeconomic conditions and
conditions in agriculture include Schultz, Hathaway, Tweeten (1980b),
Tweeten and Plaxico, Gardner(1981a). and Shepard and Collins. Schultz
presents evidence that over the period 1911 - 1942 farm and non-farm
net per capita incomes rose and fell together but the fluctuations in
agriculture were much greater. One of his tables, indicating the
magnitude of the fluctuations in the incomes of agricultural and non-
agricultural households, is reproduced in Table 7.2 below. Schultz
concluded that dependence upon an industrial economy subject to sharp

reversals of fortune may be "the Achilles' heel of agriculture".4

153

 

 

 

 

 

 

 

 

 

Table 7.2 - Cyclical Movements in Per Capita Farm and Non-Farm
Income(a)
Per Capita Net Income Per Capita Net Income
of Persons on Farms of Persons Not on Farms
Percent Change from Percent Change from
Period(b) First to Last Year First to Last Year
of Period of Period
1911 1919 +160 +88
1919 1921 -62 —18
1921 1929 +87 +22
1929 1932 —67 -52
1932 1937 +153 +59
1937 1938 —19 -7
1938 1943 +213 +101
a. T.W. Schultz, Agriculture in an Unstable Economy, McGraw
Hill Book Co., New York, 1945, p. 214.
b. The periods were chosen on the basis of changes in direction

of per capita income levels. Thus. 1929 represents a peak in
per capita income growth and 1932 the bottom of a period of
decline.

Hathaway, writing an update of Schultz' Agriculture in an

Unstggle Economy in the late 19508, continued the theme of the

importance of the performance of the non-farm economy for agriculture's

well-being. He found that during periods of general economic

recession, yields per acre fell, probably because farmers applied fewer
The decline in

units of variable inputs, especially purchased inputs.

production resulted in falling farm incomes.

Instability in the economy as a determinant of farm income
seems to have been a less dominant theme in the 1960s. Undoubtedly
this was because of the relatively high level of performance of the

economy during this period. But, with an increase in the volatility of

macroeconomic performance in the 19703 and early 19803, the literature

is once again examining the link between the macro~economy and

agriculture.

Given the long debate on this topic. it is interesting that

154

there is little agreement as to its validity. Table 7.3, updates Table
7.2 and indicates that during the period from 1940 to 1981. the
performance of the agricultural sector ceased, in a strict sense, to
follow the non-agricultural sector. From 1940 through the early 1950s
the pattern observed by Schultz continued to hold: the farm and non-
farm sectors expand and contract together and the swings in the farming
sector are wider. From 1954 through 1981 the non-agricultural sector
experienced a period of continuous expansion of disposable income. The
farm sector had a period of sustained growth from 1959 until 1973 but
experienced several up and down cycles on either side of this growth
period. Over the period 1954 to 1981, if the periodic down turns in
the agricultural sector are ignored, the net increase in disposable
income was greater for farmers than non-farmers. However. the fact
that numerous cycles were experienced in farming while the non-farm
economy continued to grow indicates that factors in addition to
macroeconomic performance must be at work in determining the health of

agriculture.

155

Table 7.3 - Cyclical Movements in Per Capita Farm and Non-farm
Disposable Income (From All Sources)(a)

 

 

 

 

 

Per Capita Disposable Per Capita Disposable
Income of Persons on Income of Persons Not
Fgrms on Fgrms
Percent Change from Percent Change from
Period! First to Lest Year Period First tongst Yegg
of Period of Period
1940—1948 +265 1940-1948 +104
1948-1949 -16 1949—1949 -.15
1949-1951 +25 1949—1953 +24
1951-1955 -12 1953-1954 -.12
1955—1958 +22
1958-1959 -6
1959-1973 +383
1973-1974 -5
1974-1975 +7
1975—1976 -7
1976-1979 +75
1979-1980 -12
LI980-1981 +17 1954—1981 +424

 

 

 

 

a. Disposable Income = Gross Farm Income less Production Expenses less
Net Income of Non-resident Operators plus Wages, Salaries and Other
Income of Farm Residents.

Source: "Economic Indicators of the Farm Sector: Income and

Balance Sheet Statistics, 1981”. Table 65, U.S.D.A.. ECIFS 1—1.

Washington, D.C. 1982, page 89.

B. Gardner (1981a). Firch and Shepard and Collins all
estimated regression equations in an attempt to identify the various
components of commodity market instability. Firch found the business
cycle to be the most important variable over the period from 1966 to
1975. Both Gardner and Firch downplay the importance of macroeconomic
conditions. They feel that with the many automatic stabilizers built
into our economy since the early 1960s, the business cycle should be of
diminished importance in explaining changing farm incomes. Firch
believes that the business cycle variable in his equation is picking up

some of the variability of foreign demand which accounts for its

significance.

156

Shepard and Collins use business failures in the non-farm
economy as a proxy for macroeconomic conditions. They report that this
variable was positively related to farm failures and conclude that the
economic well being of agriculture i§_ dependent upon macroeconomic
conditions. The exact relationship between farm and non-farm conditions
is unclear. It could be, as Firch argued. that non-farm failures are
the result of the variability induced by changes in foreign trade.

However. the general economy is not only the market for most
agricultural output, is is also a major source of employment for farm
families. The degree to which farm families are dependent upon off-farm
sources of income is illustrated in Table 7.4. The numbers in Table
7.4 indicate that an amazing transition has taken place in farming,

especially for the two middle groups. Even for the largest group of

farms, off-farm income is approaching one—fifth of total gross income.
Because of the increased importance of off-farm earnings and because of
the increased volatility of the macro—economy, Breimeyer feels we are
entering the "macro phase" of agricultural policy". Central to this
phase is the premise that what is good for the economy as a whole is
good for agriculture. This is quite similar to the view expressed by

Schultz and Hathaway.

157

Table 7.4 - Income from Off-farm Sources as a Percentage of
Total Income for Four Sizes of Farms. (Classes Based on
Value of Sales).

 

 

 

 

 

Year $100.000+ $40.000—$99.999 $10.000—$39.999 $9.999—
1969 7.2 15.7 31.1 93.5
1970 8.2 16.2 32.7 95.6
1971 8.2 17.4 37.1 99.5
1972 7.5 16.1 37.1 98.0
1973 6.5 16.0 42.8 96.9
1974 7.5 21.4 _50.2 101.3
1975 7.6 23.9 58.0 103.5
1976 9.0 28.0 66.3 105.5
1977 10.4 32.0 73.7 107.5
1978 10.0 29.7 71.2 104.2
1979 12.5 38.0 82.4 103.5
1980 14.3 50.4 95.2 104.5
1981 17.1 69.1 108.5(a) 105.5
SOURCE: "Economic Indicators of the Farm Sector: Income and

Balance Sheet Statistics. 1981", Table 57, U.S.D.A. ECIFS 1-1,
Washington, D.C.. 1982.

(a) A figure greater than 100 implies that money was lost in the
farm operation.

Tweeten (1980b) argues that the avenue by which instability
in the macro~economy is transmitted to the farm economy is the
inflation rate. In estimating the relationships between aggregate
supply and demand and farm-level supply and demand, he found all
functions except farm level demand to be homogeneous of degree zero.
He found that farm level supply adjusted to inflation more rapidly
than farm-level demand. Therefore, prices paid by farmers tended to
increase more rapidly than other prices in the system and resulted in
a cost-price squeeze on the producer. Another viewpoint is presented
by Lama and Westcott. Using a three stage least squares analysis, they

tested the hypotheses that price increases at the farm level are

rapidly passed through to the retail level and that farm level prices

determine retail prices as part of a price "mark-up" pricing system.

158

Their results indicate that virtually all price increases experienced
by farmers are passed on to the retail level within three months, with
most adjustments being made in the first month. One quarter was the
longest lag that was significant in their analysis. They present
evidence to support their hypothesis about the unidirectionality of
influence. If this were true the implication would be that farm prices
and farm costs adjust over time at roughly the same rate. If prices
paid and received did in fact move in harmony, farm incomes would be
expected to remain relatively content. This is not consistent with
history.

In summary. the discussion of the importance of the business
cycle in determining the well—being of the farm sector is inconclusive.
The empirical work done to date has not resolved othis issue
satisfactorily though the direct relationship between the economy as a
whole and the farming sector, as hypothesized by Schultz, is not as
evident as it was in earlier periods. Regardless of the degree to
which general economic conditions determine the well—being of the
agricultural sector, it is unlikely that revenue insurance will alter

the relationship. Revenue insurance is unlikely to be a major factor

in determining the course of the business cycle since the agricultural
sector is but one small component of the entire economy. Revenue
insurance would be expected to reduce the impact on the farm population

of instability transmitted from the general economy.

Foreign Trade
While foreign trade is indisputably a portion of the macro—

economy. the policy response to foreign trade induced instability will

159

differ from the response if domestic instability is the villain. For
this reason it is useful to separate the discussion of the impact of
foreign trade on instability in agriculture from the discussion of
broader macroeconomic factors.

From the end of World War Two until the late 19603, U.S.
agricultural exports were hampered by a domestic agricultural policy
that maintained domestic prices above the world price and used trade
barriers to protect the farming sector. Many of our exports during
this period required export subsidies to find a market. Schuh (1974)
argues that another major factor in the relatively poor showing of our
exports during this period was an overvalued dollar. He argues that
agricultural exports increased over the 19503 and 19603 mainly because
technological change was able to counterbalance the overvalued dollar.
With the devaluations of 1971 and 1973 and the adoption of floating
exchange rates in April 1973. the dollar should have ceased to be
overvalued. It is probably not coincidental that U.S. exports expanded
dramatically over the course of the 19703. From 1950 to 1972 the

compounded annual growth rate of the value of agricultural exports was

5 By

1980 one out of every 3.5 acres planted was for export marketse.

7.0 percent. From 1972 to 1980 this growth rate was 22 percent.

According to Houck (1979) soybeans and feedgrains accounted for 2/3 of
the value of our exports in 1978. The U.S. exported "40 percent of the
wheat. 70 percent of the corn and nearly 80 percent of the soybeans"

that entered international trade in the late 19703.7

It is highly
probable that the trend reversals that occurred in farm income in the
19703. (See Table 7.3 on page 166), are the result of this increased

reliance on foreign trade.

160

D. Gale Johnson (1982) attributes growth of U.S. exports
during the 19703 to the devaluation of the dollar. increased imports by
the centrally planned economies and increasing incomes of middle income
countries such as OPEC nations and some Asian and Latin American
countries.

Returns from exports were quite volatile in the 19703 as is
indicated in Figure 7.1. Three variables are typically used to explain
the variation noted in these graphs. D. Gale Johnson (1975)
hypothesizes that a portion of the observed variability is explained by
improved control of trade on the part of some countries, especially the
European Economic Community (EEC), the U.S.S.R. and its East European
allies, and China. The isolation of these countries from most of the
adjustment costs associated with international trade is significant
because, according to Johnson's estimates. they account for roughly
one-half of the total amount of grain traded in the international
market. In support of this hypothesis Steele estimated that during the
period from 1963 to 1975, 80 percent of the deviation from trends in
world wheat exports are explained by changes in the importation levels
of the Soviet Union and 90 percent by changes in the importation levels
of all centrally planned economies. Grennes. Johnson and Thursby
constructed a simulation model to estimate the price effects in major
importing and exporting countries that would result from a ten percent
increase in the imports of the U.S.S.R.. given current "restrictive"
trade policies. Their results indicate that wheat prices in the U.S.,
Canada and Australia. the major exporting nations, would increase by
17.5 percent, 5.7 percent, and 7.0 percent respectively. The EEC. with

its protective tariffs and variable levies, would experience a price

161

increase of only 3.5 percent.

A second major source of variability in international
agricultural commodity markets is the exchange rate. Empirical
investigations into the importance of exchange rates have been done by
Chambers and Just, Johnson, Grennes and Thursby and Collins, Meyers and
Bedahl. The most interesting result noted by these studies is that the
effects of exchange rate changes on international trade, are crop
specific. That is. the impact of exchange rate movements on wheat may
be dissimilar to the effect on cotton. Chambers and Just found that
exchange rate changes were extremely successful in explaining short
term variations in wheat and soybean exports, and only slightly less
successful with respect to corn. They found that inventories of corn
and wheat were very sensitive to exchange rate movements while soybeans
were more sensitive to changes in domestic consumption. In estimating
the elasticities of these three crops with respect to the exchange
rate, they found that short term export elasticities for wheat and corn
were greater than one, in absolute value, but less than one for
soybeans. They conclude that "exchange rate fluctuations (have) had a
significant real impact on agricultural markets by altering the volume
of exports and the relative split between exports and domestic use"
with respect to wheat, corn and soybeans.8

Johnson. Grennes and Thursby built a model of world wheat
trade which differentiates wheat by point of origin to test the
hypothesis that exchange rate changes could explain price increases
for wheat in 1973/74. They failed to find support for the hypothesis.
In commenting upon this result. Chambers and Just note that this static

result actually conforms to their expectations in that they found the

162

long run exchange rate elasticity of price to be less than one for
wheat.

Finally, Collins, Meyers and Bedahl note that exchange rate
movements are rarely, if ever. consistent across currencies. For
example, through the 19703 the dollar depreciated against most
currencies in Western Europe but appreciated against many of the
currencies of less developed countries. Since the mix of products
purchased by developed and less developed countries is different, with
LDCs importing relatively more wheat and cotton while DCs purchase
mainly corn and soybeans. different exchange rate impacts should be
expected. They found that exchange rate changes could explain a
relatively small portion of real price changes for wheat, corn or
soybeans but a large portion for cotton. They concluded that. except
in special cases, exchange rate movements are unlikely to be the
driving force behind changes in commodity prices in the U.S. Again,
this result does not necessarily conflict with the findings of Chambers
and Just since it refers to a longer term impact.

A third source of agricultural export instability of
increasing concern is the issue of non-tariff barriers (NTBs). As
Hillman points out. NTBs are an especially difficult issue to
analyze because there is little by which you can evaluate them. They
tend to be more administrative in nature and hence are more removed
from the public eye than are tariffs. Many NTBs can be implemented by
the executive branch without a specific mandate from the legislative
branch of government. Hence, NTBs can be instituted. changed,
rescinded or otherwise amended with greater flexibility, some might say

capriciousness, than tariffs which often require legislative approval

163

for amendments and are subject to international agreements such as the
Generalized Agreement on Tariffs and Taxes. In addition, even if NTBs
do result from a law or proclamation that specifies their function, the
letter of the law is much less important than how it is carried out.
Needless to say. NTBs are a very thorny issue in trade negotiations.

In summary, economic theory has long touted the benefits of
trade. A world with free trade was suppose to be the best of all
possible worlds since both parties to a trade are made better off. The
volatility of agricultural markets during our recent past has caused

9 In the

many to appreciate the costs as well as the benefits of trade.
U.S. trade fluctuations have contributed to variations in farm income.
I believe that a substantial portion of the observed variability in
export markets arises from the inability to anticipate political
decisions which affect them. When the Soviet wheat crop failed for two
consecutive years in the early 19708, the market had no way of knowing
that the Kremlin would reverse the long established practice of
slaughtering livestock to reduce the grain deficit and instead go onto
the world market to satisfy their requirements. Likewise, when the
Soviet Union invaded Afganistan. the markets could not have known that
President Carter would place an embargo on wheat sales to the U.S.S.R.
The markets cannot anticipate the imposition of a NTB or an importation
quota. If markets cannot predict these types of events. and such
events result in instability in commodity markets, it is difficult to
imagine that revenue insurance could do much to reduce this source of
instability. One of the primary selling points of a revenue insurance

program is its ability to transmit market signals which tell the farmer

to expand or contract production. But agriculture is based on

164

biological processes which cannot be speeded up. Adjustments to new
market conditions take time. If political decisions profoundly affect
the terms of trade and the market is unable to transmit signals to
farmers in advance of these actions, revenue insurance will not enhance
the ability of farmers to make adjustments reducing the magnitude of
changes in market conditions wrought by the political decisions. As
was the case with instability generated by changes in the general
economy. the principle effect of revenue insurance on instability
caused by international markets will be to reduce the impact of this

instability on the welfare of the farm population.

165

The Industrialization of Agriculture

Carter and Johnson feel that the industrialization of
agriculture. with its increased market orientation, is the most
significant change in American agriculture since the advent of the
tractor. During this process agriculture went from a situation in
which the farming unit was extremely self-reliant to one in which it
purchased most of its needs. Farmers began purchasing electricity from
the Rural Electrification Administration. horsepower from John Deere or
others, seeds from Pioneer. Dekalb and others. transportation from
General Motors. desserts from Pepperidge Farms, credit from the
Production Credit Association and labor from the United Farm Workers.

Harrington calculated production expenses as a percentage of
gross farm income for selected years between 1935 and 1981. In 1935,
production expenses were 53 percent of gross income. by 1981 they had
grown to 88 percent for the average farm. Farms with sales of greater
than $100,000 tended to have a higher ratio of expenses to gross sales
than did smaller farms. Harrington believes that this increased
dependence upon and commitments to outside sources of inputs makes a
farm less flexible and more sensitive to exogenous shocks. In the
past, during hard times and when starting out in farming, farm families
survived by cutting back on cash expenses and using greater discretion
in how they used their inputs. They tightened their belts. Today,
there are fewer notches left in the belt. Farmers have less control
over their business. This greater exposure to exogenous shocks. when
combined with the increased dependence of the farm population on off-
farm sources of income, seems to lend support to hypotheses discussed

earlier which stressed the importance of the business cycle or foreign

166

trade in determining the economic health of the food system.

One result of the industrialization of agriculture has been
an increased dependence upon markets which are oligopolistic in nature
(a possible basis for Tweeten's cost—price squeeze hypothesis).
Another result is that fewer people see agriculture as a unique sector
of the economy. Prior to the integration of agriculture into the
broader economy. policy makers routinely gave agriculture special
consideration. Agriculture was endowed with a set of institutions
designed to cope with its special requirements (the federal farm credit
system, land grant universities. the U.S.D.A. and so on). Legislation
routinely exempted farmers from policies felt to be unduly burdensome
on them (minimum wage. child labor laws, the draft, accrual
accounting, anti-trust, etc). Most of these special provisions
continue to exist but there is also a growing current of protest from
non-agricultural sectors of the economy about the special treatment.
Another indication of the diminished sympathy for the idea that
agriculture is unique is the proliferation of voices involved in
agricultural policy and the way in which the agenda for policy debate
is determined. Far from being cognizant of any unique characteristics
of agriculture, policy debates are, according to Infanger et. al., now
determined by budgetary considerations completely divorced from any
policy goals.

Finally, industrialization has increased the degree of
specialization in farming. As farmers have expanded the size of their
operation in an effort to take advantage of economies of size , they
become more reliant on the performance of a single market. This

would be expected to increase the variability of revenue earned.

167

Revenue insurance is yet another off-farm input and an
additional cash expense. However, by assuring a given minimum return,
revenue insurance might counteract some of the increased vulnerability
caused by the industrialization process. This is a variant of the
earlier discussion regarding cash flow problems. Revenue insurance
would be expected to enhance the economic survivability of the farm by
several means. First. insuring a minimum level of income increases the
likelihood that cash expenses will be met. Second, the ability of
farmers to plan investments and obtain credit should be enhanced by a
revenue insurance program. Finally. while a specialized farm would
still be dependent upon the long term health of the market for its
output. the impact of short term deviations from trends would be

reduced.

Chronic Excess Supply

Another explanation of instability focuses on the volatility
of supply. Supplies of agricultural commodities vary over time for a
variety of reasons: cycles. environmental factors, public policy
changes and so on. If demand is relatively stable. changes in supplies
will dramatically alter the returns to agricultural commodities since
most face relatively inelastic demand curves.

Sandmo, in a theoretical consideration of production under
uncertainty, concluded that if uncertainty is reduced, production will
expand. This would seem to lead to the conclusion that revenue
insurance might exacerbate the problem of surpluses. This is likely to
be a short term result only since expansion of production would.

ceteris paribus. be expected to reduce the price received for the

168

commodity that is in surplus. The response should be a reduction in
output of that commodity. By increasing the strength of market
signals, revenue insurance should reduce the problem of chronic
oversupply. These adjustments will, of course. take time and will
entail significant costs for the farm population.

Surpluses can also be of a more acute nature, as in the case
of cycles. It has been suggested that revenue insurance would increase
the potential for planning by farmers. To the extent that this occurs.
coordination in the food system would be expected to improve and cycles

to diminish. The validity of this hypothesis is an empirical issue.

Summary and Conclusions

This chapter discussed two problems facing agriculture,
examined competing hypotheses about the causes of these problems and
the effect a revenue insurance policy may have on these problems. The
first issue examined was entry barriers in agriculture. The major
cause of barriers to entry in agriculture. high start-up costs. is
associated with high land prices. Evidence was presented indicating
that land prices are high because returns to investments (in the form
of the value of agricultural output, tax advantages and capital gains)
are high. Because returns and expenses occur at radically different
points in the investment period. outside income is necessary in the
early years of a land purchase. The group least able to compete for
land is likely to be young farmers trying to enter farming. The impact
of revenue insurance on the issue of entry barriers is ambiguous though
there is evidence indicating that revenue insurance might reduce the
problem.

Instability in agricultural markets was discussed in some

169

depth. My conclusions are that macroeconomic conditions and foreign
trade in particular. have increased the degree of instability witnessed
in agricultural markets. With bigness and specialization comes
increased reliance upon off-farm inputs and upon the performance of a
single market. The result is an increased vulnerability to exogenous
shocks. The ability of revenue insurance to alter the conditions
underlying instability is limited. It will, however. have an important
role in reducing the costs associated with instability. This is of
particular importance at the level of the individual farm. It bears
repeating that the principle of insurance is to take a small amount of

money from a large group so that the losses of a small subset can be

compensated. Revenue insurance would reduce the impact of market
instability on the welfare of the farm population. It would not cure
the disease but would treat the symptoms. To the extent that

instability is caused by inability to plan investment decisions.
revenue insurance should enhance planning potential and hence reduce

the instability observed in commodity markets.

In the closing chapter, the conclusions reached will be
summarized. recommendations concerning the feasibility of revenue

insurance made and future directions of research noted.

170

. See the Detroit Free Press, September 23, 1982 and April 3, 1983.

. Robison, Lindon and John R. Brake, Dec. 1980, page 132.

. Harris. Duane G., 1977, page 1106.

. Schultz. T.W.. 1945, page 128.

. O'Brien, Patrick M.. 1981, page 13.

. O'Brien, ibid page 3.

. McCalla. Alex F. and Andrew Schmitz, 1979, page 1022.

. Chambers. Robert G. and Richard E. Just. 1981. page 44.

. See Warley for a brief discussion of this view of trade.

Chapter 8

Summary. Conclusions and Issues for Further Research.

This chapter summarizes the results of earlier chapters and
evaluates of the strengths and weaknesses of the revenue insurance
program. Finally. issues within this topic area and methodological

questions needing further consideration will be addressed.

Summar

In Chapter 2 the historical records of a number of public
insurance programs were examined. Successful programs tend to be based
on the individual's personal experience as directly as possible, settle
claims promptly. have easily understood provisions and have few close
substitutes. The coverage must also protect a variable of concern at a
sufficiently high level to gain and hold the interest of the buyer.

Based on these characteristics a revenue insurance program
was proposed. This program would offer coverage based on an
individual's gross farm receipts from all farming activities in a
single crop cycle. Coverage levels would be a percentage of average
returns over a base period (ten years) and would be adjusted over time
to account for inflation and changing risk structures. Policies would
be sold and serviced by private insurance companies with reinsurance
services offered by the federal government. Premiums would at least

cover indemnities.

171

172

In the third chapter the economic and psychological
approaches to the study of insurance were examined. Economists have
improved our understanding of the causes of adverse selection. moral
hazard. the importance of information to sellers (in terms of types
required and the timing of acquisition) and the importance of
considering more than observed behavior in determining the risk
attitudes of individuals.

Psychologists have provided valuable insights into human
behavior in uncertain environments. Psychologists have. for example.
highlighted the inclination of consumers to buy insurance for high
probability-low cost risks. the importance of framing and the limited
ability of people to process and utilize statistical information in a
dynamic context.

Economists have been criticized because empirical work has
provided convincing evidence that the assumptions about behavior
frequently employed by economists don't bear a close resemblance to
actual consumer behavior. Psychologists have been criticized because
it is difficult to falsify. in the sense of Popper. their propositions
(eg. Prospect Theory). Both schools, though imperfect. have provided
insights that should prove useful to a policy designer contemplating a
revenue insurance program.

In Chapters 4 and 5 mean variance models of demand and
supply were developed for a revenue insurance market. The results of
these models indicated that demand for insurance will increase as a
buyer becomes more risk averse. as the loading factor used to calculate
his premium falls or if there is an increase in the size and likelihood

of receiving an indemnity. The seller's side of the market is more

173

complex but it was concluded that the seller will increase the level of
coverage offered if his clients become more risk averse. if he becomes
less risk averse or if the correlation between his clients' outcomes
decreases. The most important conclusion about this market was the
strict interdependence between the two sides of the market. Because of
this interdependence the actions of either the seller or the buyer
cannot be considered in isolation from the other.

Chapter 6 summarized the empirical phase of the study.
Support for the theoretical models of the two previous chapters was
found. The field work indicated revenue insurance might be less
expensive to operate. in terms of indemnity payments, than anticipated.
Furthermore, relatively high levels of participation could be attained
at premiums that would more than cover indemnities. This is an
indication of the viability of the program. The appeal of revenue
insurance does not appear to be limited to any single class of farms
(classified by number of acres).

Finally. in chapter seven the role of revenue insurance in
farm policy was examined. Revenue insurance is not a panacea for the
diverse challenges facing U.S. agriculture. Two examples of current
farm problems. entry barriers and unstable commodity markets. were
discussed. The conclusion reached is that revenue insurance will
reduce the impact of these problems as experienced by the individual
farm, but will not eliminate these issues.

An Evaluatioggof Revenue Insuggggg_

Many positive characteristics of a revenue insurance program

were discussed in this thesis. First. it offers coverage on a variable

that is of greater direct interest to farmers that do current programs.

174

Second, the emprirical investigation indicated that the cost of
providing this type of protection could be less than anticipated from
the point of view of the farmer and the government. Annual average
indemnities received were less than $8.00 per acre for all farms in the
sample. In addition, farmers indicated a willingness to pay a premium
in excess of what would be needed for actuarial fairness meaning a
portion of the administrative costs of the program could be covered by
premiums collected.

A third aspect of the program that is encouraging is that it
seems to attract participants from farms of many different sizes. In
addition. younger farmers may have a greater propensity to purchase
revenue insurance. If revenue insurance increases the ability of a
farm to weather bad economic times, the higher propensity of younger
farmers to purchase insurance could have important structural
consequences for agriculture.

The revenue insurance program has the very attractive
feature of linking management decisions and program benefits. A
program such as deficiency payments or even the Grain Stabilization
Program of Western Canada have an important weakness: the actions of
the individual farmer have relatively little impact on the amount of
the benefits received or the cost of protection. For example. a
deficiency payment is received by a participating farmer if he has
complied with the planting. tending and harvesting requirements set
forth in the program and the price for his crop is below a pre-
specified level during the first five-months of the marketing season.
His past management decisions will be partially reflected in the base

upon which his benefits are calculated. But, the amount per bushel he

175

receives is based less on his actions than upon the aggregate actions
of all farmers producing his crop. In addition, each participant pays
the same percentage cost to participate, regardless of farm size or
riskiness of production. Thus, if a ten percent set-aside is required.
every participant takes ten percent of his land base out of production.
A revenue insurance program, as discussed in this thesis, would tie
both benefits and costs to management decisions of the individual
farmer client. This would offer the possibility of sending powerful
market signals, in the form of a higher premium or lower insured level.
to farmers whose management decisions are out of line with prevailing
market conditions.

Of course, the program is not without its drawbacks. One
problem is the large amount of disinterest in the program indicated by
the high proportion of farmers who refused to participate in the
study. Even those who did participate voiced a great deal of
skepticism about the program. A good deal of the negative response to
the idea of revenue came from the impression that revenue insurance
would remove the "right to fail” from farming. Many seemed to think of
the program as a form of agrarian welfare that would undermine the
moral fiber of rural America.

Another issue concerns the equity of a revenue insurance
program. In Chapter 7 it was argued that a significant portion of the
variability in agricultural markets comes from fluctuations in foreign
trade and general economic conditions. If the farmer is not in any way
responsible for a large part of the instability he experiences, yet is
asked to pay a premium covering all the costs associated with this

variability, there is a question about the justness of this solution.

176

As noted by Viscusi in Chapter 3, it is only by changing the insurance
premium that insurance can indirectly affect the causes of risk.
Since many of the factors which determine the riskiness of a farmer's
revenue experience are beyond his control and not affected by changes
in his behavior, this may lessen the amount of market information that
can be transmitted by the insurance premium. Specifically, the
management decisions of a single farmer in Iowa will have little
influence on how Washington determines monetary, fiscal or trade policy
and even less over similar decisions taken in the capitals of our major
trading partners. Yet, these exogenous decisions will affect the level
and variability of his earnings and, thereby, affect his insurance
costs and coverage levels.

There is also a question about the longer term impact of
revenue insurance on bid prices for agricultural land. If revenue
insurance increases the stability of returns in agriculture, this might
make investments in agricultural land more attractive. In short, the
dynamic response of the system to revenue insurance could exacerbate
the problem of entry barriers.

Finally, a number of adminstrative issues were raised but
left unanswered. The most vexing of these questions is how to deal
with beginning farmers and those who undertake a major reorganization
of their operation. In both cases the data required to establish an
insurance program based on the client's characteristics is lacking.

My bottom line on revenue insurance is that it is a
promising program that contains some very challenging design problems.

It is a program that merits serious consideration and further study.

177

Methodological Issues

There are three fairly obvious methodological issues arising

from this study: data issues, testing the reformulated model and
broadening the empirical base. All insurance programs are heavily
dependent upon an accurate data base. It is from such a base that
actuarial tables are constructed. This data base does not exist for a
revenue insurance program. Part of the reason for this lies in the

fact that the data needed, revenue earned from each crop cycle,
frequently are not kept by farmers. A second part of the problem is
that where they do exist, a significant proportion of farmers would be

reluctant to divulge such data. Data collection will be difficult. On

the one hand, this seems to be an insurmountable obstacle to
implementation of a revenue insurance program. This assessment is
modified somewhat by two considerations. First, data of equal or

greater sensitivity and detail are routinely demanded and received by
financial institutions which deal with farmers. Coordination between
bankers and revenue insurance sellers would seem to offer substantial
benefits to both parties. The second consideration is the
communications revolution, as represented by the personal computer,
that is progressing through the farming community. If, as is likely,
home computers become as prevalent on the farms of the future as four-
wheel drive tractors are on the farms of today, the maintenance,
storage, retrieval and transmission of farm records will be greatly
facilitated. The data problems may be overstated.

In the meantime, tax records, though a poor substitute,
might provide sufficient data for inauguration of the program.

Availability is still an issue with tax records. If the program is

178

begun with tax data, it should be understood that after each year of
operation a year of tax based data would be removed from the data base
and a year of crop cycle data added. Less than optimal performance of
the program might be expected until a good data base is developed.

The model developed in the empirical chapter needs
additional field testing. The tests to which it was put in this
dissertation were inadequate for the obvious reasons that direct farmer
participation was not involved and the sample size was too small. It
would be foolhardy to launch a major new policy on the basis of the
results from fifteen or twenty farms. A broader sample would provide a
better test of the model, better data from which to draw aggregate
results and more information about particular portions of the farm
population (eg. young farmers) about whom we have special interests.

Aggregate results might be obtained without more fieldwork
in the following way. A number of studies have been done on the risk
aversion coefficients of farmers. In addition to this study, King,
Love, Carmen and Cochran all did this type of research while at
Michigan State University. There is a great deal of consistency in
their results, leading to the conclusion that there is a fairly stable
distribution of attitudes toward risk in the farming population of
Michigan. A PDF over risk aversion coefficients could be constructed
from the work cited above. This could be combined, via a Monte Carlo
routine, with data from Michigan State University's farm record-keeping
program. Telfarm, and the models developed in this thesis to generate
premium projections for a much broader sample of farms. In addition,
Telfarm records have data on inventory changes, so a much better

picture of the crop cycle earning record of these farms could be

179

achieved than was possible with tax-based data. To the extent that
these farms are representative of farms in the U.S. and the
distribution of risk aversion coefficients is representative of risk
attitudes of farmers in general, valuable insights into the functioning
of a revenue insurance program could be gained at relatively little

additional cost.

Revenue Insurance Program Issues

In the final analysis every model is a gross simplification
of reality. The degree to which it captures essential elements of
behavior will determine its usefulness. There is no substitute for
experience with a program, however, in determining crucial performance
characteristics. Models such as those constructed in this work, help
focus attention on aspects of likely importance but, as we have seen,
they often raise as many issues as they answer. The task force
commissioned to study revenue insurance suggested implementation of a
three-year revenue insurance pilot program. While a three year program

for insurance is somewhat of a contradiction of the philosophy of

insurance. which depends upon long run probabilities for its
livelihood. a pilot program could be a very useful experiment. It
might answer some of the behavioral issues raised in this thesis. It

could also help determine the acceptability of this approach to the
farm population.

The ultimate cost and effectiveness of a revenue insurance
program depends upon the details of the institutional design. In
particular, the existence of other government programs, such as the
current commodity programs, will profoundly influence the operation of

a revenue insurance program. Part of the reason for the relatively

180

stable revenue records of farmers is the existence of commodity
programs during the base period. For participants in these programs
they provided a means of achieving price insurance. For non-
participants, target prices also helped stabilize prices by providing
a point of resistance below which market prices could fall only with
difficulty. If revenue insurance is implemented as a substitute for
these other programs, an increase in the degree of variability in
agricultural markets would be expected. The extent of increase is
difficult to determine and is a question the pilot program would be
incapable of addressing.

In conclusion, there are aspects of the program that some
people will find appealing. Other people will find those same aspects
unappealing. Whether revenue insurance could serve a useful role in

the bundle of programs used in agricultural policy will, like all

policies, depend as much upon the wisdom of the person designing the
program as upon the inherent worth of the idea. There are many
uncertainties associated with any idea that will restructure property

rights. One result of this was noted by Machiavelli,1

"There is nothing more difficult to arrange, more doubtful of
success and more dangerous to carry through than to initiate a new
order of things. . . Men are generally incredulous never really
trusting new things unless they have tested them by experience.”

181

Machiavelli's conclusion has particular relevance for revenue
insurance. There are powerful interests likely to be opposed to the
idea while prospective proponents are dispersed and made mute by the
uncertainties of a new program. The prognosis for implementation of a
revenue insurance program is not good, at least in the short run. In
view of the problems facing agriculture, however, it is not an idea

that can or should be abandoned.

 

1. From The Prince as quoted by Mancur Olsen, 1983, page 58.

APPENDICES

182

APPENDIX 1

Properties of the truncated mean:

(1)

(2)

(3)

(4)

(5)

Given that the truncated mean is deiined as:

us . auP + Y - V(aflP - Y > - c
2 A l

dP*/da 8 (l - !)(flP + an(3P/Ea) + (EY lid) + V(EY /9a)

2 i
but BP/ia I “4(afl)
and BY lie 8 -afl¢f(afl)
2
and BY lie 8 afl26(afl)
i
so dfl*/da I PP(1 - P) < 0

dF*/dY I aP(1 - !)(3fl/EY ) - DY /3Y ) + i + (iP/BY )(afl(l - V)
2 2 l 2 2

dfl*/dY 0
2

but if dP/dY 5 0
i

and dfl/dY = 0
I

then dF*/dY > 0

dF*/dv a Y - aflP < 0
1

(l - !)a(P + “(SP/39) + EY /3“ + VBY l?“
2 l

dF*/dfl

I aP(i - 9) < 0

II
I
pu-
A
CD

dF*/dC

183

Preperties 04 the truncated variance:

Given that the variance is defined as:
0*2 - (afl)2P(i - P) + 02 + “2(1 - P) - Y2 - ZaflY P
2 2 2

(6) d0*3/da 3 (de/da) - “2(dP/da) + 2a33P(1 - P) + “3(dP/da)
2

* (afl)3(1-2P)dP/da - d(Y )3/da - ZFY P - ZaflP(dY /da)

2 2 2
- ZaflY (dP/da)
2
but de/da 8 -(afl)2f(afl)(u)
2
and d(Y )2/da 8 2Y (-afl24(afl))

and, dY /da and dP/da are as previously defined.
2

Therefore,

0.
do*1/da - 2flP afl - Y )f(Y)dY < 0
IF
(7) do*2/dY - 2E (Y2)/3Y ) + (al)2(i - 2P)(3P/3Y ) +
2 2 2 2

22fl2P(1 - P)(2P/3Y ) - 2Y - ZaIflP + Y P(3fl/2Y ) +
2 2 2 2

FY (EP/EY ) 0
2 2

(8) d02/dfl 8 2aF3P(1 - P) + (afl)3(l - 2P)(3P/3fl) - BYz/fl +
2

3E (Y2)/3F - 2a(Y P + “Y (SP/9“) + FP(3Y /3fl))
2 2 2 2 2

8 22P<afl(i - P) - Y ) ( 0
2

184

APPENDIX 2

Since
dCE I 0 I i - 9 - X(afl(i - P) - Y )
2

We can determine the relationships between the optimal coverage ratio
and the other variables in the model by taking the total differential
of this first order condition with respect to the coverage ratio and
the other parameters.

Pr ertie f h ti 1 ev l f v r f r R'sk Av r i i n
Hgkgr

(1) 63CE I 0 I I-xfl(i - P)Jda f I-lld!

so (da/d!) I 1/(-xfl(1 - P)) ( 0

(2) d3CE I 0 I I-XF(1 - P))da t I-(afl(l - P) - Y )Jdl
2

so (da/dx) I (afl(l - P) - Y )/(-xfl(1 - P)) ) 0
2

(3) d3CE I 0 I I-xfl(l-P)Jda f I(iL/EF)(afl(1-P) - Y ) - x(a(i-P))Jdfl
2

if (2k/2I) S 0 then (da/dfl) < 0

if (ah/2P) ) 0 then (da/dfl) 0

(4) 630E I 0 I I-xfl(i-P)lda t I-{(ix/3Y )(aP(l - P) - Y ) +
2 2

x(a(2fl/2Y )(1 - P) - aF(2P/2Y ) - 1)}1dY
2 2 2

(da/dY ) I [(EX/EY )(afl(1 - P) - Y ) + X(a(3F/2Y )(1 - P) -
2 2 2

afl(2P/2Y ) - l)1/I-XF(1-P)] 0
2

185
APPENDIX 3

As noted in the text of this chapter, only substitution
effects on optimal levels of insurance coverage will be considered.
When income effects are added most of the results are ambiguous.
Considering only substitution effects, the first order condition (FDC)
for the optimal coverage ratio offered by the seller is:

S n B
dCE /da I 0 I (“(Y P - 22FP<1 - P)) + Y (i - P))](X azx )
2 1 i=1 i i

S n n n
- x I(F(l - P)(aHP - Y )(X 22 f 2 X X P a a )
1 iIi i iIi JIifi ii i J

S 2 2 2
- (A /2)((afl) P(1 - P) + E (Y ) - Y - 2aFY (l - P)) *
l 1 I

n ll
(2 x z a a (29 /Ga)l
i=1 Jam 5 .i ii

In the text, of this chapter one case in which (3P lia) might be
iJ

greater than zero, moral hazard, was noted. For the purposes of this

appendix, it is assumed that this partial derivative is zero. If the

total derivative of this expression with respect to 'a' and buyer i’s

risk aversion coefficient is taken, the resulting expression is:

2 S n B
(I) d CE I [X ¢2x fl3{f(afl)(Y - Y - afl(l - 2P)) - 2P(l - P))

iIi i i 2 l
S n n n
- x “ZIP(1 - P) - f(afl)(aflP - Y )(X «3 + 2 X X P a a ))lda
i iIl i iIl iIifl ii i J
n B
f [2 azfltY P - 2aFP(1 - P) + (1 - P)Y )ldx
iIi i 2 1 i

Or, in a shorthand notation:

2 S B
d CE I 0 I Inida + [saidx
i

186

Which means
8
(da/dx ) = -[**]/[x]
i

Since the term [*1 must be negative to be at a maximum, the sign of
this ratio will depend upon the sign of the numerator. From the FDC we
S

know [as] must be positive since the term multiplied by x in the FCC

is positive. This being the case, [is] must be greater than zero in
8

order to satisfy the FCC. This means the (da/dx ) will be positive and
i

an increase in buyer i’s risk aversion means the seller will offer a

higher coverage level.

In the derivatives to follow we will continue to use the
symbol [*1 to represent the derivative of the first order condition
with respect to the coverage ratio.

The derivative of the FCC with respect to a and a is:
i

2 S n B
(2) d CE I [*Jda + IZPI X a x (Y P - 2aPP(l - P) + (i - P)Y }
iIi i i 2 i
S n n
- x {(1 - P)(aPP - Y )(X a f X P a ))llda for J I i
i iIl i JIifi ii J i

Again, in the shorthand notation,

2 8
d CE I [elda + Imelda
i

Ol‘,

(da/da ) I -[**l/I*J
i

The sign of this derivative is ambiguous since both terms that make up
[as] are positive and one is subtracted from the other. The sign of

the term, therefore, depends upon the relative magnitude of these two
factors.

The derivative with respect to the optimal coverage ratio and
the mean outcome of the uninsured distribution is:

187

2 S n B
(3) d CE I [*lda + [2 «2x (an(aP)(Y - Y + aP(2P - 1)) f
iIi i i 2 l

S

Y P + Y (i - P) - 4aPP<i - P)) - x {(aPP - Y )2
2 i i
n
(i - P - an(aP) + aPPii - P))(X «2
iIi i
n n

e 2 X 2 P a c )}ldP
iIi infi ij i i
or
2 S
d CE I 0 I [*lda f [fildfl

and
(da/dfl) I -I**l/I*l

Again, this is ambiguous because the sign of the term [as] is unknown.

The derivative of the FCC with respect to the coverage ratio
and the seller’s aversion to risk is:

2 S n
(4) d CE I 0 I [*lda + [-(P(i - P)(aPP - Y )(X a3 f
l iIi i
n n S

2 2 X P a a ))1x
iIi ism ij i ,i

or
2 S S
d CE I 0 I [*lda - [asidx

and since the term If!) is positive, the expression

8
(da/dx ) I I**]/Iil ( 0

This simply says that as the seller becomes more risk averse he will
try to limit his exposure to risk by reducing the proportion of his
clients’ PDF that he is insuring.

The derivative of the F00 with respect to the coverage ratio
and the correlation coefficient will be:

188

2 S S n n
(5) d CE I [elda - I-2x {P(i - P)(aPP - Y )(X 2 a a )}ldP
l iIi infi i J iJ
so 2 S
d CE I 0 I [*lda - [*ildP
iJ
and (da/dP ) I [asl/I*l < 0
iJ

This result also has intuitive appeal. If the outcomes of
the insurance pool become more highly correlated, the insurer will
reduce his exposure to risk by reducing the coverage ratio offered. An
increase' in the correlation coefficient increases the variance of the
seller’s returns without changing his expected returns. For this
reason, it is understandable that the insurer would chose to reduce the
coverage offered as P increases.

IJ

And last, but certainly not least, the derivative of the FDC
with respect to coverage and the average outcome over the uninsured
portion of the distribution will be derived. This is by far the most
complicated of the total derivative expressions. It may be expressed
as:

2 S n
(6) d CE I [*lda f I(BP/BY ){(Y P - 4aPP(i - P) + Y (1 - P))(X «2x )
2 2 l iIi i i
S n n n
- x (X c3 f 2 X X P a a ) * (22PP(1 - P) - Y (i - P))) f
iIi i iIi JIifl iJ i J i
n B
+ (BF/BY ){P(Y - Y - 2aP(i - 2P))(X mix ) - (2P2(i - 2P) - FY ) a
2 2 i iIi i i i
S n n n
x (2 a2 f 2 X X P a a ))
iIi i iIi infl ij i J
n 8 S n n n '
+ (OY /2Y )(P(l - P)(X mix + x (2 e3 + 2 X X P a a )}
i 2 iIi i i iIi i iIi JIifi ii i J
n B
+ PP: «2x ldY
iIi i 2

In general, this derivative cannot be signed.

B I BL I OGRAPHY

189

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