Peter E. Hildebrand
THE UNIVERSITY OF CHICAGO
THE THEORY OF CrOP INSUiANCE
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE SOCIAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF ECONOMICS
HAROLD GRAHAM HALCROW
In my study of literature prior to writing this disserta-
taion, it became evident that the hope and approbation with which
crop insurance was discussed had not been matched by the perfor-
mance of any crop insurance program. Because of a general lack of
theoretical analyses in the published works and because of a grow-
ing conviction that the development of the theory in realms not
heretofore explored would indicate the framework within which crop
insurance should be organized for maximum efficiency, I was
prompted to propose the present topic as the subject for a dis-
I was encouraged to proceed by Professor Theodore W.
Schultz, who told me he thought the problem significant. I was
helped by the members of my committee, Professors D. Gale Johnson,
iMilton Friedman, and Chauncy D. Harris. Professor Friedman helped
to improve the theoretical and empirical presentation in specific
instances. Professor Johnson, as chairman of the committee, made
several suggestions on theoretical argument, on organization, and
on content, which have been of great help in improving the manu-
script. Several friends and colleagues aided me through discus-
sions and correspondence.
The theory presented here may be of value in the develop-
ment of future crop insurance programs. One conclusions, for in-
stance, is that in theory the present Federal crop insurance pro-
gram cannot succeed; but there is promise for successful crop in-
surance operation under plans for area-yield insurance and for
weather-crop insurance herein described.
LIST OF TABLES .. . . . vi
LIST OF FIGURES . . . . viii
I. BACKGROUND AND PERSPECTIVE . .....
1. Purpose of Study
2. Scope and Outline
3. Some Definitions and Assumptions
II. THE CASE FOR CROP INSURANCE . . 10
1. Effects of Yield Variations on Farmers'
2. Effects of Yield Variations and of Yield
Uncertainty on Resource Utilization
Time and flexibility
Present and future technology
Price certainty for factors
3. Attempts to Establish Crop Insurance
III. INSURANCE GUItES APPLIED TO CROP INSURANCE 28
1. The Insurable Interest
2. The Importance of the Risk
3. The Cost of Crop Insurance
4. The Number of Risks
5. The Mathematical Calculation of Risks
IV. CROP INSURANCE BASED ON INDIVIDUAL FARM YIELDS. 42
1. The General Theory and Assumptions
All Basic Assumptions Fulfilled
Technical and Technological Conditions
Base Yields for Farms and County Are
Not the Same
All Farmers Do Not Purchase Insurance
Farmers Grow Two or More Crops
2. All-Risk Crop Insurance and Resource
V. AREA YIELD INSURANCE . . .60
1. General Concepts
The Normal Yield
The Current Yield
The Insured Yield
2. General Theory and Assumptions
Technical and Technological Conditions
Mean Yields for Farms in the Area
All Farmers Do Not Buy Insurance
3. Effects of Area-Yield Insurance on
4. Illustrations and Criticism
5. Some Special Problems of Area-Yield
Localized Insect Infestations
Changing Cost-Price Relationships
6. Adapting Area-Yield Insurance to All Crops
in the Area
Basing Insurance on Yields of One Crop
Basing Area-Yield Insurance on Two or
Basing Area-Yield Insurance on Weighted
Average of Crop Yield
VI. WEATHER-CROP INSURANCE . . .. 84
1. General Concepts
The Formula for Indemnities
The Insured Yield
2. The Construction of a General Formula
Precipitation and Yields
Temperature and Evaporation
3. A Test Case
4. Summary of Advantages and Disadvantages
Conditions of Adaptability
VII. RECOMMENDATIONS APPLICABLE TO THE FEDERAL CROP
INSURANCE PROGRAM . . . . 115
1. Practices and Techniques
2. General Philosophy and Procedure
3. The "Fixed Price" Amendment
4. Some Suggestions for Further Research
Development of Area-Yield Insurance
Normal area yield
Premiums and insured yields
Development of Weather-Crop Insurance
The formula for indemnities
Premiums and indemnities
5. General Conclusions
SELECTED BIBLIOGRAPHY. . . . 129
LIST OF TABLES
1. Yields of Spring Wheat at Belle Fourche, South
Dakota, and Computed Income Expectancy of a
Farmer Receiving These Yields, Assuming Stable
Prices and Costs .* * * 12
2. Summary of Federal Wheat Crop Insurance,
1939-1936 . . . . . 27
3. Typical Operating Expenses of the Federal Crop
Insurance Corporation Under Conditions Assumed . 37
4. Classification of 1269 Farms in Chouteau County,
Montana, According to Average Wheat Yields
1925-1932 . . . . . 48
5. County Premium Rate, Average Base Yields and
Average Insured Yields, in Chouteau County,
Montana, for 1947, in Bushels per Acre . . 48
6. Illustration of Effects of Area-Yield Insurance
on Wheat Yields of Farms in Pratt County, Kansas,
Assuming All Farmer Insure for IMan Area Yield . 72
7. Wheat Yields per Seeded Acre on Five Farms in
Alton Community, Fergus County, Montana. .* 73
8. Wheat Yields per Seeded Acre on Five North
Dakota Farms . . . . . 74
9. Correlation Between Soil Moisture in the Surface
Three Feet of Soil at Seeding Time and Yield of
Winter Wheat . . . . . 91
10. Probabilities of Obtaining Specified Yields of
Winter Wheat When the Soil was Dry or Wet to
Designated Depths at Seeding Time . . 91
11. Summary of Average Yields of Spring Wheat When
the Soil at Seeding Time was Wet to the Depth
Specified . . . . . 92
12. Correlations Between Preseasonal Precipitation,
August to November, and Yields of Spring Wheat
at Experiment Stations in the Great Plains . 95
13. Correlations Between Preseasonal Precipitation,
August to March, and Yields of Spring Wheat at
Experiment Stations in the Great Plains . . 95
14. Correlation Coefficients for Yield and
Precipitation for Four Crops in Three Areas of
Central South Dakota, 1919-1943, Inclusive .
15. Correlation Between Annual Precipitation and
Yields of Spring Wheat at Experiment Stations
in the Great Plains .... ......
16. Comparison of Estimated Yield with Actual Yield
for Stations in the Northern Great Plains .
17. Effects on Yields of Use of Weather-Crop
Insurance at Belle Fourche, South Dakota ...
18. Effects on Cash Returns of Use of Weather-Crop
Insurance at Belle Fourche, South Dakota .
& 0 .
LIST OF FIGURES
1. Average effect in bushels per acre of an
additional inch of rainfall in a five-day period
on the yield of spring wheat from continuously
cropped plots at Dickenson, North Dakota . . 101
2. Average effect in bushels per acre of an
additional inch of rainfall in a five-day period
on the yield of corn from continuously cropped
plots at Wooster, Ohio . . . . 102
3. Average effect in bushels per acre of an
additional inch of evaporation in a five-day
period (influence of associated rainfall being
eliminated) on yield of spring wheat from
continuously cropped plots at Dickenson,
North Dakota . . . . 106
BACKGROUND AND PERSPECTIVE
This is a study in applied theory in which we are concerned
with the application of economic theory to the problem of insuring
crops or crop yields against the occurrence of adverse physical
phenomena, such as "bad" weather, insect infestations, and general
crop diseases, which may periodically depress crop yields. Crop
insurance is conceived as a device which may be used by a farmer
to protect himself against partial or. complete crop failure to the
extent that this failure is due to the adversity of physical crop
conditions which are beyond his control. We seek to investigate
and to develop the forms that crop insurance so conceived may take
in order to satisfy certain standards of operation as these are
1. Purpose of Study
Crop insurance has been discussed for many years and nu-
merous articles have been written on the subject; but the published
materials have largely neglected the formal aspects of the theory
which may be associated with the subject. Little has been done,
therefore, to outline the theory of crop insurance in a manner
which may help to determine what type or kind of crop insurance
can best meet the needs of farmers and can be sold most profitably
or with least subsidy. This lack of analysis may have resulted
from (1) the difficulty of bridging the gap between the short-run
dynamics, so apparent in agriculture, and the long-run statics of
equilibrium theory, and (2) the fact that crop insurance presents
what seems to be a peculiarly complex and difficult problem in
Although a farmer may have a "good idea" of what his yields
will average over a period of years he cannot know what his yield
will be in any one future year or in any particular series of years
because the yield will be influenced by conditions not known prior
to the development of the crop.1 As a consequence of this lack of
knowledge, farmers tend to follow a rigid pattern in their produc-
tion plans,2 and changes in total output that do occur are largely
due to the incidence of weather and of disease or insects asso-
ciated with certain kinds of weather.3
We assume, therefore, that the function of crop insurance
should be (1) to measure the degree of yield variation inherent in
the effects of weather and in disease or insects associated with
certain kinds of weather, and (2) to distribute the cost of this
1There is evidence that corn-belt farmers expect the mean
of future yields to follow trends in past yields with small modi-
fications for improvements in technology and varieties. See
Theodore W. Schultz and 0. H. Brownlee, "Two Trials to Determine
Expectation Models Applicable to Agriculture," Quarterly Journa
ofD Ennc nis, LVI (1941-42), 487-496. For models to be used in
studying anticipations see G. Tintner, "A Contribution to the
Non-static Theory of Choice," ibid., pp. 302-304.
20ther factors also contribute to this rigidity. (1)
Farmers are uncertain about future prices. (2) There is some in-
security in farmers' financial position. (3) Capital rationing,
increasing risk, and lack of equity financing, combine to prevent
expansion when a consideration of net marginal return indicates
expansion might be required to maximize net return. (4) The pro-
duction of some crops involves a high proportion of fixed costs.
Cf. D. Gale Johnson, Forward Prices for Agriculture (Chicago: The
University of Chicago Press, 1947), pp. 43-120, 158, 159.
3Agriculture in the United States exhibits a tendency to-
ward stability in total volume of products marketed. See Theodore
W. Schultz, Agriculture in an Unstable Econnmy (New York:t iGraw
Hill Book Company, 1945), pp. 10-45 and Sherman E. Johnson, Changes
in Farming in War and Peace, FM58 (Washington: United States De-
partment of Agriculture, Bureau of Agricultural Economics, June
1946), pp. 64-69.
variation in some equitable manner among all farmers buying crop
The purpose of this study is to develop the general theory
related to crop insurance in order to determine what forms crop
insurance programs may take in best fulfilling the above functions.
2. Scope and Outline
An application of economic theory must be based on certain
value judgments.2 Value judgments must be used to determine what
the significant problems are and to define the policy or program
to which the theory may be applied. This study is based on several
value judgments, one of the first being that crop insurance should
be offered to a farmer as a voluntary, rather than as a compulsory
contract.3 Crop insurance, if on a voluntary basis, presents few
conflicts of interest. Measures designed to help stabilize indi-
vidual farmers' incomes are widely accepted as a desirable part
1Crop insurance should not be designed to protect a farmer
against yield losses which are due to his own mismanagement, be-
cause to do so would tend to penalize one farmer and to aid another
indiscriminately. Cf. Schultz, op.,it., pp. 217 and 218.
2Value judgments are a part of welfare economics, the
function of which is to determine the ideal conditions necessary
for the attainment of the ends which society holds. Thus in a
study in applied theory one must hold certain welfare concepts or
make certain judgments of what is desired in order to establish a
framework within which the proposals or rules for action can be
developed. For example, as in the case of the income tax, the
school lunch, reclamation, conservation, etc., one must hold some
concept of what is desired in order to determine a framework within
which to work. Once this framework is established it may be neces-
sary to make other value judgments in order to determine what is
"good". This again determines the theoretical outline for applied
economics. For more complete discussion see for example A. C.
Pigou, The Economics of Welfare (London: Macmillan and Company,
1920), pp. 3-106; 111-113; 691-798; and 893-911.
3A strong case might be made for the use of compulsory
crop insurance and/or for the use of some subsidy. For example
of precedent and general arguments see ibj., pp. 902-911.
of agricultural policy.1 Hardship of a most acute nature has been
experienced by large numbers of farmers as a result of erratic
yields. In addition sharp changes in individual farmers' incomes
have caused hardship for those doing business with farmers. If
crop insurance can reduce fluctuations in farmers' incomes and can
improve resource utilization in agriculture, and if it can be made
to function on a voluntary basis, it should be accepted generally
as a desirable tool of agricultural policy. In this study, there-
fore, we proceed directly to the realm of application in which
rational rules or precepts for action can be formed.
The first four chapters are introductory. In Chapter II
we present the case for crop insurance (1) by illustrating the
effects of yield variations on a farmer's income, (2) by deter-
mining the probable effects of yield variations and of yield un-
certainty on resource utilization by the firm, and (3) by reviewing
some of the attempts which have been made to establish crop
Chapter III presents the basic concepts of general in-
surance which may be considered in a program of crop insurance.
A discussion is undertaken to determine how crop insurance pro-
grams should be developed to conform with these concepts.
In Chapters IV-VI we outline specific types of crop in-
surance programs. Three types or forms of crop insurance pro-
grams are considered.
The first type of crop insurance, discussed in Chapter IV,
is based on individual farm yields, with premiums and indemnities
related to these yields. This resembles the "all-risk" insurance
ISee for instance, Theodore W. Schultz, o.Rit., Chapter
X; J. S. Davis "American Agricultures Schultz' Analysis and
Policy Proposals The Review of Economic Statistics. XXIX (1947),
89-91: John D. Black "Professor Schultz and the C.E.D. on Agri-
cultural Policy in 1 45," Joual of Far nomcs XXVIII (1946),
682,686; D. Gale Johnson, oncit., Chapters XII and XIII.
which has been tried in the United States since 1939 and which has
been administered by the Federal Crop Insurance Corporation. The
analysis proceeds on the basis of various assumptions. It is as-
sumed, first, that the insuring agent or insurance carrier has
perfect knowledge of the yield history of the individual farm.
This assumption is next replaced with the assumption that the in-
surance carrier does not have accurate knowledge of individual
farm yields. This opens the analysis to the study of adverse se-
lectivity among the insureds.1 The general effects of this type
of crop insurance on intensity of cultivation, on cropping prac-
tices, on rotations, and on the general farm plan are considered.
The analysis of resource utilization is applied successively (1)
to a single crop farm, and (2) to a farm which grows more than one
crop but has only one crop insured, or has just part of the crop
acreage insured. We attempt to determine in theory whether this
type of insurance can be sold successfully or not.2
The second type of insurance, discussed in Chapter V, is
based on area yields.3 The principle of this plan is that pre-
miums would be paid to insure a given average yield for an area.
Indemnities would be paid to all insured farmers when the average
yield for the area fell below the insured base average for the
area. The adequacy of this insurance for stabilizing income is
Adverse selectivity, as used above and in the discussion
which follows, refers to the situation existing when relatively
poor risks become dominant among the insured groups. The position
is taken that adverse selectivity can exist only when there are
faults in the theory or practice of establishing premiums relative
to probable indemnities.
2See below, this Chapter, Part 3, for definition of terms.
3For brief summary of a plan to be based on area yields
see Andrew R. Aandahl, "A Crop Insurance Proposal," Jwaa Frm
Science, Vol. I, No. 2 (August 1946), 12-13.
The third type of insurance, discussed in Chapter VI, is
based on weather phenomena.1 The principle of this plan is that
premiums are assessed to insure against the occurrence of certain
weather phenomena which are adverse to crop production such as
hail, excess rainfall, deficient rainfall, wind, heat, etc. In-
demnities would be paid after the occurrence of adverse weather.
Various formulas are tested. A scale of premiums and indemnities
is established for a farm.
Chapter VII concludes the dissertation with a summary of
recommendations which may be applicable to the United States crop
insurance program. Some consideration is given to issues of agri-
cultural policy which are related to crop insurance.
3. Some Definitions and Assumptions
Crop insurance is defined as the insurance of crop yields,
according to some measurement, against the effects of adverse
weather. As indicated above, the basis for measurement may be
(1) individual farm yields, (2) area yields, or (3) the weather
itself. The three types of crop insurance are referred to, respec-
tively, as (1) all-risk crop insurance, (2) area-yield insurance,
and (3) weather-crop insurance.
Following general insurance terminology each farmer that
may be covered with an insurance contract is called "an insured"
and each insured may be referred to, sometimes, as "a risk". The
person or institution selling the insurance may be called "the
insurance carrier" or "the insurer".
Risk and uncertainty are terms which have been used to
describe the nature of expectations or anticipations. Risk has
1For brief discussion of a plan based on state averages
see Fred H. Sanderson, "A Specific-Risk Scheme for Wheat Crop
Insurance," Journal of Farm Economics, XXV (1943), 759-776.
been defined by a certain group of writers to include expecta-
tions or anticipations which are based on a probability distribu-
tion having known parameters, and uncertainty has been defined to
include expectations or anticipations which are based on a proba-
bility distribution of probability distributions.2 Whether this
distinction between risk and uncertainty is a useful one or not
depends on the context within which the terms are used. As has
been pointed out,3 the important distinction between risk and un-
certainty does not depend on the fashion in which expectations
are "catalogued." Rather, it depends on the effect of the phe-
nomena described on the operation of the firm. It can be argued
that there is little reason for distinguishing between the opera-
tion of the firm under risk and under uncertainty unless it is
1See for example, A. G. Hart, "Risk, Uncertainty and the
Unprofitability of Compounding Probabilities," Lange, et al (ed.),
Studies in Mathematical Economics and Econometrics (Chicago: The
University of Chicago Press, 1941), pp. 110-116; A. G. Hart, "An-
ticipations, Uncertainty, and Dynamic Planning,,Studies in Busi-
ness Administration, XI, No. 1 (Chicago: The University of Chicago
Press, 1940); A. G. Hart, "Uncertainty and Inducement to Invest,"
Review of Economic Studies, VIII (1940), 49-53; E. Lindahl, Studies
in the Theory of Money and Canital (London: George Allen and Unwin
Ltd., 1939), pp. 348 ff; Frank H. Knight, Risk. Uncertainty and
Profit (Boston: Houghton Mifflin Co., 1921; reprinted by London
School of Economics, 1933), pp. 197-232; G. Tintner, "A Contribu-
tion to the Non-Static Theory of Production," Lange, at al (ed.),
Studies in Mathematical Economics and Econometrics (Chicago: The
University of Chicago Press, 1941), pp. 92-109; G. Tintner, "The
Theory of Choice Under Subjective Risk and Uncertainty," Econome-
trica, IX (1941), 298-304; G. Tintner, "The Pure Theory of Pro-
duction Under Technological Risk and Uncertainty," bd.,, pp. 306-
21bre specifically, Hart and Tintner have adhered to this
definition of uncertainty while Knight (ib.i., pp. 233-234) de-
fined uncertainty as existing when there was lack of knowledge
concerning the actual probability distribution. For example see
A. G. Hart, "Risk, Uncertainty and the Unprofitability of Com-
pounding Probabilities," on. cit., p. 110 and G. Tintner, "The
Pure Theory of Production Under Technological Risk and Uncer-
tainty," op. cit., p. 305 and G. Tintner, "A Contribution to the
Non-Static Theory of Production," opcit., p. 92.
3See D. Gale Johnson, op. ott., p. 38, Cf. Hart, "Risk,
Uncertainty and the Unprofitability of Compounding Probabilities,"
on. cit., p. 110.
assumed that the firm can adjust to take advantage of improvements
in expectations in one case but not in the other.
In the theory of production which follows, therefore, risk
is applied to the situation in which no decisions can be deferred,
with technological risk the amounts of the commodities to be pro-
duced and the factors expected to be used over the interval n' + 1,
n' + 2, .., n appear as functions of the prices, accumulation
rates, and technical and technological coefficients as well as the
amounts of products expected to be produced and of factors expected
to be used over the interval 1, 2, ., n'. The plan which is
laid for the interval 1, 2, .., n' must be carried over to cover
n' + 1, n' + 2, ., n.
Uncertainty is applied to the situation in which some deci-
sions can be deferred in order to take advantage of new or more
accurate knowledge. The production plan can be changed at the end
of each of the n'-th periods. Technological risk, therefore, ap-
pears as only a special case of technological uncertainty.
The common situation in crop production is technological
uncertainty when a series of years are considered. Risk, rather
than uncertainty, may be applied to the farmer's production plan
in any one given year. The distinction seems relevant to the
theory of crop insurance only because it may help to clarify the
problem involved. One of the first principles of insurance is
that risks can be classified so that a common premium rate will
apply to all those cases falling within the same probability dis-
tribution. One of the difficulties in some kinds of crop insurance,
however, is that the probability distribution of losses changes
with every season. The situation facing the insurance carrier,
therefore, has some of the elements of uncertainty. To function
without adverse selectivity, however, insurance must be sold under
a situation in which the mathematical expectation of indemnity is
the same for all insureds paying similar premiums. How to achieve
this latter state is one of the basic tasks of this study.
In order for crop insurance to be called "successful" or
to be considered "to work" as mentioned above, the conditions es-
tablished require (1) that crop insurance cover major losses
arising directly from Adver~e weather phenomena, and (2) that pre-
miums be made low enougkt to attract a large percentage of farmers
and high enough to insure coverage of actuarial probabilities of
loss over a period of years plus costs of administration. This
second condition requires that premiums be accurately determined
to reflect loss probabilities for each group or class of farms
insured. These criteria do not exclude the possibility that there
could be a "run" of years in which premiums would exceed indem-
nities, and vice versa, but they do require that adverse selec-
tivity be eliminated and that losses due to bad management be
separated from those due to weather.
THE CASE FOR CROP INSURANCE
The nature and importance of the case for crop insurance
will be indicated (1) by illustrating the effects of yield varia-
tions on a farmer's income, (2) by determining the probable effects
of yield variation and of yield uncertainty on resource utiliza-
tion by the firm, and (3) by reviewing some of the attempts which
have been made to establish crop insurance systems.
1. Effects of Yield Variations on Farmers' Incomes
Yield variations of crops have been the subject of several
investigations.1 Some of the reasons for yield variations have
been catalogued.2 Without an exhaustive analysis of these studies,
1See for example V. P. Timoshenko, "Variability in Wheat
Yields and Outputs," Wheat Studies of the Food Research Institute,
XVIII (1942), 291-338. See especially appendix and bibliographical
note, pp. 331-338.
Marion Clawson, "Sequence in Variation of Annual Precipi-
tation in the United States," The Jonrnal of Land and Public
Utility Economics, XXIII (1947), 271-287; John S. Cole, Correa-
tions Between Annual Precipitation and the Yield of Sring Wheat
in the Great Plains, U.S.D.A. Technical Bulletin 636 (1938);
A. L. Hallsted and E. H. Coles, "A Preliminary Report on the Rela-
tion Between Yield of Winter Wheat and Moisture in the Soil at
Seeding Time," Journal of Agricultural Research. XLI (1930), 469-
473; John S. Cole and 0. R. Mathews, Relation of the Depth to which
the Soil is Wet at Seeding Time to the Yield of Spring Wheat on the
Great Plains, U.S.D.A. Circular 563 (May 1940); A. L. Hallsted and
0. H. Mathews, Soil Mbisture and Winter Wheat with Suggestions for
Abandonment, Kansas Agricultural Experiment Station Bulletin 273
(1936); George A. Rogler and Howard J. Haas, "Range Production as
Related to Soil ~bisture and Precipitation on the Northern Great
Plains," Journal of the American Soniety of Aeronomy, XXXIX (1947),
378-389; Ray F. Pengra, "Correlation Analysis of Precipitation and
Crop Yield Data for the Sub-humid Areas of the Northern Great
Plains," ibid., XXXVIII (1946), 848-850.
the effect of yield variations on a farmer's income can be indi-
cated by an illustration (see Table 1).1
The variations in yields, shown in Table 1, may be large
compared with variations expected in some other areas,2 but these
variations may be of lesser magnitude than those experienced by
many farmers, particularly the farmers in semi-arid regions.3 The
income variations, shown in Table 1, are of such magnitude that the
farmer would be facing considerable income uncertainty. While im-
pacts of these variations might be counterbalanced in part by main-
taining large reserves of cash or bonds, etc., and/or crops in
storage, the farmer might best stabilize his income expectancy by
use of an acceptable form of crop insurance.
2. Effects of Yield Variations and of Yield
Uncertainty on Resource Utilization
The effects of yield variations on resource utilization are
not as simple to show as are the corresponding effects on farm in-
come because the manner in which the farmer will combine resources
depends, in part, upon the farmer's individual capital position,
his psychological reaction to uncertainty in both prices and yields,
the peculiar rigidities and frictions that may exist toward re-
source utilization in the industry, and the variations in yield
and price expectations that may be motivating. As may be evident
to most observers, the variations that do occur in yields and
prices tend to bring about many peculiar patterns of resource
utilization. Some resources in agriculture are rationed while
iFor another illustration based on county averages see
Carl P. Heisig, "Income Stability in High-Risk Farming Areas,"
Journal of Warm Economics, XXVIII (1946), 961-972. County data
may not indicate the magnitude of the variations of yields on a
2As shown by Timoshenko, on. 0 it., pp. 334-337.
3f. Heisig, loc. cit.
YIELDS OF SPRING WHEAT AT BELIE FOURCHE, SOUTH DAKOTA, AND
COMPUTED INCOME EXPECTANCY OF A FARMER RECEIVING THESE
YIELDS, ASSUMING STABLE PRICES AND COSTS
I Available for Net Return
Family Living, for Management
Interest, after all
Gross Cash Income Taxes, Expenses
Year Yielda Returnb Costs and DenreciaticM and Charge
1908 21.7 $10,850 $4,085 $ 6,765 $ 3,765
1909 28.7 14,350 4,435 9,915 6,915
1910 2.6 1,300 3,650 -2,350 -5,350
1911 0 0 2,500 -2,500 -5,500
1912 0 0 2,500 -2,500 -5,500
1913 10.8 5,400 3,540 1,860 -1,140
1914 10.1 5,050 3,505 1,545 -1,455
1915 57.6 28,800 5,880 22,920 19,920
1916 17.3 8,650 3,865 4,785 1,785
1917 7.4 3,700 3,370 330 -2,670
1918 11.9 5,950 3,595 2,355 645
1919 .9 0 2,500 -2,500 -5,500
1920 29.9 14,950 4,495 10,455 7,455
1921 7.3 3,650 3,365 285 -2,715
1922 32.2 16,100 4,610 11,490 8,490
1923 28.0 14,000 4,400 9,600 6,600
1924 21.5 10,750 4,075 6,675 3,675
1925 19.8 9,900 4,990 4,910 1,910
1926 31.3 15,650 4,565 11,085 8,085
1927 21.6 10,800 4,080 6,720 3,720
1928 32.9 16,450 4,645 11,805 8,805
1929 28.3 14,150 4,415 9,735 6,735
1930 15.4 7,700 3,770 3,930 930
1931 .5 0 2,500 -2,500 -5,500
1932 17.7 8,850 3,885 4,965 1,965
1933 16.5 8,250 3,825 4,425 1,425
1934 12.4 6,200 3,620 2,580 420
1935 6.9 3450 3_.345 105 -2.895
Avg. 17.5 I $8,747 4- 03,857i $4,890 I $1,890
aAverage yields, in bushels per acre, received on 30 plots,
with 5 plots on fallowed ground, 4 on green manured land, 12 fol-
lowing corn, 1 following sargo, 1 following potatoes, 3 following
oats, and 4 continuously cropped to wheat.
bOn basis of wheat selling at $1.00 per bushel throughout
and constant seeding of 500 acres.
cIncludes constant cash cost of $5.00 per acre prior to
harvest, harvesting expense of $1.00 per acre plus 10# per bushel.
dIncludes $1,500 for family living and $1,500 for interest
and depreciation but no charge made for income taxes.
Source of data on yields: John S. Cole, Correlations Be-
tween Annual Precipitation and the Yield of Spring Wheat in the
Great Plains, U.S.D.A. Technical Bulletin 636 (1938), p. 6.
others may be underemployed.1 In many cases, farmers lack capital.
Some farmers may not know the merits of better practices. Others
may not be able to do a better job because of the tenure situation.
in which they find themselves. The combined effects of yield and
price variation and uncertainty have no doubt distorted the use of
resources in agriculture to the extent that these resources are not
used in a manner which would maximize their value for the people
in agriculture or for the general welfare.2
In order to test the validity of the above statements and
to determine how resource utilization may change with the decrease
in yield uncertainty that can be achieved through use of crop in-
surance, it may be expedient to attempt a short review of the
theory of the firm giving special emphasis to phases of the theory
which may be affected by the use of crop insurance. We shall first
outline the theory of the firm operating under certainty, there-
fore, and then compare this with an outline of the theory of the
firm operating under uncertainty. The purpose of this review is
to help lay a rigorous foundation for the theory of crop insurance.
1Definitions of rationing and underemployment are based on
a consideration of marginal returns. The evidence that capital
is rationed in agriculture is attested by the fact that earnings
of capital in agriculture are frequently higher in rate than are
earnings outside of agriculture. See D. Gale Johnson, on. cit.,
pp. 62-71. Likewise there is evidence of low earnings by people
employed in agriculture. See Theodore W. Schultz, on. cit.,
2Neglecting such problems as unpaid costs, which may arise
through erosion, free public services, family exploitation, and
accepting as given the distribution of resources among individuals,
we may define an optimum utilization of resources as a condition
that exists when any small change in the production pattern leads
to a combination of decrements and increments in output such that
there is no system of exchanges whereby the increments will be
accepted voluntarily as compensation for the decrements. Of.
iilton Friedman, "Lerner on the Economics of Control," The Journal
of Political Economy, LV (1947), 406. According to this defini-
tion it seems evident that resources in agriculture are not used
in a manner to maximize their value, although, it should be remem-
bered also that yield and price variations and uncertainties are
not alone responsible for this failure.
A simplified theory of the firm based on single valued
anticipations can be constructed for conditions of perfect com-
petition with the assumptions (1) that a definite price or series
of prices can be anticipated, (2) that there is a single known
production function, and (3) that one factor, entrepreneurship,
is indivisible and is subject to a rising supply price, and that
the entrepreneur maximizes his satisfaction.1
Under the above assumptions, the necessary condition for
equilibrium is that the value of the marginal product of each fac-
tor should equal the price of the factor.2 To establish that this
is a point of equilibrium it is sufficient to determine that (a)
the value of the marginal product resulting from the increased use
11t is necessary to add this third assumption in order to
achieve a determinate solution. Kaldor has demonstrated that the
firm would disappear under static equilibrium conditions which in-
clude certainty and perfectly devisable resources. Therefore the
third assumption is justified on grounds of expediency even though
it may be unrealistic because, if the first two assumptions are
fulfilled, there would be no real job for an entrepreneur. See
N. Kaldor, "The Equilibrium of the Firm," Economic Journal, XLIV
(1934), 60-67. Also it is desirable to assume that the entrepre-
neur maximizes satisfaction instead of profits, in this case, be-
cause profits are zero, which may be maximum, under perfect
2This assumes perfect competition in the sale of the pro-
duct and perfect competition and an unlimited budget in the hire
of factors. With a limited budget, capital rationing, the firm
will be in equilibrium when the values of the marginal products
are proportional (rather than equal) to the factor prices. Dia-
grammatically, when the market for the sale of the product is im-
perfect while factors are purchased in a perfectly competitive
market, marginal value added by the factor must equal price of the
factor. If the market for the sale of the product is perfect while
factors are purchased in an imperfect market the value of the mar-
ginal product of each factor must be equal to the marginal cost of
the factor. These solutions may be generalized for imperfect com-
petition in buying and selling by saying that the necessary condi-
tion for equilibrium is that the marginal revenue which may be at-
tributable to a unit of factor is equal to marginal cost of that
factor and it may be sufficient (a) that a particular marginal cost
curve intersect the corresponding revenue curve from below, and
(b) that the aggregate of all marginal costs intersect the marginal
revenue curve from below.
of any one factor will be less than the cost of that factor, and
that a decrease in factor input will reduce total revenue more than
total cost, and (b) an equal proportionate increase (or decrease)
in all the variable factors will decrease (or increase) the average
value of the product produced per unit expenditure on variable
factors.1 There can be more than one maximum if the entrepreneur
is indifferent to the additional effort which might be required at
some higher levels of output, or if he attaches some utility to
non-pecuniary gains. The determinate position can be established
by conceding that the entrepreneur works to maximize satisfaction,2
that he has a rising supply price, and that increased efforts are
required on his part to reach higher levels of output.3
Either static or dynamic conditions can exist with single
values anticipations of price and with single valued technological
1See J. R. Hicks, Value and Capital (Oxford University
Press, 1939) pp. 78-88 or J. E. Meade and C. J. Hitch, An Itro-
duction to Economic Analysis and Policy (New York: Oxford Univer-
sity Press, 1938), pp. 155-158.
2T. de Scitovszky has remarked that the assumption of pro-
fit maximization is based on observation and is, therefore, an
empirical law which need not apply to every entrepreneur and may
be untrue about a typical representative. It is not inconsistent,
however, with the general statement that the individual maximizes
his satisfaction which can be accepted as a first approximation
in the development of a theory of the firm. See T. de Scitovszky,
"A Note on Profit Maximization and Its Implications," Review of
Economic Studies, XI (1943-44), 57-60, and K. E. Boulding, "The
Incidence of a Profits Tax," The American Economic Review, XXXIV
(1944), 567-572, See also Frank H. Knight, Risk, Uncertainty, and
Profit, op. cit., Chapters III-VI.
3The development in this paragraph runs parallel to that
presented by D. Gale Johnson. See D. Gale Johnson, "The Theory of
Forward Prices for Agricultural Products," unpublished Ph.D. Thesis,
Iowa State College, Ames, Iowa, 1945, pp. 13-17. It is not in-
tended that the general theory of the firm be developed here. Only
those aspects of the theory which may be related to crop insurance
are discussed. Interest centers chiefly in how the firm reacts to
technological uncertainty as contrasted with its behavior under
technological certainty. Once this is outlined attention may be
directed to the reactions to be experience with the suggested pro-
grams of crop insurance. The approach is intended to be utili-
tarian. Thus it may be expedient to omit much of the general
theory which is associated with price.
rates of transformation. The static state does not require dating
whereas the dynamic state does.1
In the static state the entrepreneur is faced with (1) a
single known production function, (2) the prices of the factors,
(3) the prices of final products, and (4) the entrepreneurial re-
source. Since prices and techniques are known and do not change
the problem of the entrepreneur is reduced to routine management.
There would be a continuous flow of factors and products, and equi-
librium would be achieved by fulfillment of the necessary and
The dynamic state introduces the idea of change. It be-
comes the function of the firm to adjust for changes in prices of
factors and products and for changes in technology. The adjustment
will be made toward the changes that will be known to occur at all
future dates for which plans are made. Three factors are involved:
(1) time and flexibility; (2) present and future technology; and
(3) expected prices for factors and for products.2
Time and flexibility.--Time and flexibility must be con-
sidered because the firm, operating under dynamic conditions, must
adjust inputs, outputs, capital structure, etc., as new conditions
arise or are anticipated. The entrepreneur must decide what is to
1Some writers have introduced the idea of the stationary
state, in part because it may be less exacting in its presupposi-
tions. See for instance Theodore W. Schultz, "Theory of the Firm
and Farm Management Research, Journal of Farm Economics, XXI
(1939), 575. Schultz uses the idea of the stationary state because
it permits some dating or "periodicity in production and in con-
sumption, the requirement being that the changes be of a regular
and reoccurring kind and follow an exact and known pattern." The
difference between the stationary state and the static state is
that in the former interest and time perferences must be introduced
because of the dating and periodicity.
2For a discussion of price anticipations see George F.
Stigler, "Production and Distribution in the Short Run," Journal
of Political Economy, XLVIII (1939), 305-327; A. G. Hart, "Antici-
pations, Uncertainty and Dynamic Planning," op. cit., pp. 25-27
be done in order to maximize satisfaction.1 The frequency and
magnitude with which production circumstances change determines
the time and degree of change which must be made in the plans for
the firm. The larger and more frequent the changes in production
circumstances are, the greater must be the flexibility of the firm
in order to minimize losses over the period which plans encompass.
The function of flexibility is to reduce the relative losses over
a period of time.
Present and future technoloyv.--With certainty, both
present and future technical and technological conditions of pro-
duction will be known, but under dynamic conditions changes will
occur.2 If the time and extent of these changes are known, the
entrepreneur's task is to decide between alternative plans in order
to determine which plan will maximize his return. Under dynamic
conditions production involves a stream of inputs and outputs. To
maximize the resulting stream of surpluses over a period of time
the entrepreneur will choose the production plan which has the
greatest present net capitalized value. This involves a dis-
counting of future returns in comparison with current returns ac-
cording to interest rates and time preference. Interest enters
into the calculation under dynamic conditions and becomes more im-
portant as expectations become more precise. Interest rates are
relatively stable in agriculture, however, and the dual effects of
1Kaldor, on. cit., p. 70. ". the function which lends
uniqueness and determinateness to the firm the ability to adjust,
to co-ordinate is an essentially dynamic function ".
2For a study of dynamic production under assumptions of
technical and technological certainty see G. Tintner, "Some Remarks
on the Dynamic Theory of Production," Renort of Fifth Annual Re-
search Conference of Cowles Commission for Research in Economics
(Chicago: The University of Chicago Press, 1939), pp. 61-63;
Tintner, "A Contribution to the Non-Static Theory of Production,"
Studies in Mathematical Economics and Econometrics, Lange, et al
(ed.); on. cit., pp. 92-98; A. G. Hart, "Anticipations, Business
Planning and the Cycle," Quarterly Journal of Economics, LI (1937),
capital rationing and uncertainty reduce the interest problem in
farming to one of relative unimportance.1 The stability conditions
are similar to those for the equilibrium of the firm under static
conditions. There must be (1) an increasing marginal rate of sub-
stitution between outputs, (2) a diminishing marginal rate of sub-
stitution between inputs, and (3) a diminishing marginal rate of
transformation of an input into an output. Also the present value
of the stream of surpluses must be positive.2
Price certainty for factors and Droducts.--As with cer-
tainty of technical and technological conditions, price certainty
contributes to the refinement of marginal choices thus facilitating
optimum utilization of resources. In order to convert a static
theory of the firm to a dynamic theory, two amendments must be
made. (1) Outputs and inputs due to be sold (or bought) at dif-
ferent dates must be treated as if they were different products or
factors, and (2) actual prices must be replaced by the discounted
values of the expected prices.3 The important effect of price cer-
tainty is that the entrepreneur will begin immediately to adjust
his scale of operations according to his expectations. With price
certainty these expectations will be precise and accurate. Even
so, and as Hicks has remarked, there is no reason why production
plans should follow any simple pattern, or even why the influences
making for an increase (or decrease) in output should be dominant
at every date.4 The production pattern with price certainty could
be highly complex.
1See Theodore W. Sohultz, "Theory of the Firm and Farm
Management Research'" on. cit., p. 580.
2See Hicks, on. cit., Chapter XV (esp. p. 199) and mathe-
matical appendix pp. 319-323, 325-326.
3This discussion follows Hicks, ibid., Chapter XVI.
4bid., p. 210.
Price certainty should influence resource utilization in
agriculture in the following ways: (1) There would be a marked
improvement in utilization of resources among commercial farmers
because (a) capital rationing would be reduced, and as a conse-
quence capital would be substituted for labor in capital poor
areas, (b) the position of the small commercial farmer would be
improved relative to the larger farmer, (c) a more satisfactory
mechanism would be provided for distributing products into pro-
cessing and consumption, and (d) disinvestment in soil resources
would be retarded because cyclincal swings in land prices would be
discouraged and contractual payments would be easier to meet. (2)
Resource allocation between agriculture and the rest of the economy
would be improved providing other measures were used to improve the
mobility of labor.1
The assumptions given above are useful in outlining one
theory of the firm but they do not fit the situation which has con-
fronted the individual farmer. Farmers have found it necessary to
assume (1) that, although maximization of profit is a goal, the
goal is seldom reached because there is uncertainty and there are
inclinations to avoid risk,2 (2) that future prices are uncertain,
with prices for products being more uncertain than the prices for
1The above is a partial listing of conclusions presented
elsewhere. Cf. D. Gale Johnson, "Contribution of Price Policy to
the Income and Resource Problems in Agriculture," Journal of Farm
Economics, XXVI (1944), 635-653.
2Profit by definition arises largely out of uncertainty.
According to Professor Knight "It is not dynamic change, nor
any change, as such, which causes profit, but the divergence of
actual conditions from those which have been expected and on the
basis of which business arrangements have been made. For a satis-
factory explanation of profit we seem to be thrown back from the
'dynamic' theory to the uncertainty of the future, a condition of
affairs loosely designated by the term 'risk' in ordinary language
and in business parlance." See Knight, onp cit., p. 38,
factors, and (3) that production functions are multi-valued, with
the greatest variation in values occurring among crops as compared
with livestock enterprises, with some crops subject to much greater
variability than others, and with much of the variation in crop
yields being due to variations in weather conditions.
Profit maximization is a first approximation retained be-
cause of its usefulness.1 However, with increasing risk, which is
associated with uncertainty, entrepreneurs are apt to stop short
of the point of maximum profit.2 The determinate solution may be
at a point generally below the point of maximum profit.
As a consequence of uncertainty the farmer finds that his
capital funds are rationed. This limits the efficiency of his re-
source utilization.3 Rationing has two important consequences.
It may limit the total output of the firm and/or it may limit the
size of various enterprises. Some factors in agriculture such as
land, in cases where rented land is not readily available, and
machinery may be severely rationed while some other factors, such
as labor, are less severely rationed.
1As has been pointed out by de Scitovszky, op. cit., 51-60.
This concept of profit maximization may apply more precisely to
agriculture, because of the nature of the competition among farmers,
than to other industries in which competition is less perfect. Cf.
M. W. Reder, "A Reconsideration of the Marginal Productivity Theo-
ry," The Journal of Political Economy, LV (1947), 450-458.
2proof of this statement was undertaken by Boulding in an
analysis of the incidence of the profits tax. See Boulding,
op. cit., pp. 567-572.
3M. Kalecki, Essays in the Theory of Economic Fluctuations
(New York: Farrar and Rinehart, Inc., 1939), pp. 95-106. Some
rationing could exist even with certainty because of the imperfec-
tions in the capital market, but rationing becomes more severe as
uncertainty becomes greater. Equity financing might overcome some
of the effects of uncertainty but it has not been introduced into
agriculture largely because of the small size of farms and the re-
actions to uncertainty. Insecurity of tenure often results in pur-
chase of farm land with limited capital. This type of financing
restricts the scale of the firm and, in part, accounts for the wide
variation existing in the size of farm. See Theodore W. Schultz,
"Capital Rationing, Uncertainty, and Farm Tenancy Reform," Journal
of Political Economy, XLVIII (1940), 309-324.
The effect of rationing of the efficiency of the firm de-
pends, in part, on the degree of substitution possible among fac-
tors. In agriculture, substitution among factors is common but
there is also a general condition of factors acting in a comple-
mentary manner. This general condition exists because the factors
which may be substituted for each other under constant output may
be complements under variable output because with variable output
an increased supply of one factor may increase the marginal value
productivity and employment of another factor.1 The assumption of
variable output implies a greater tendency toward complementarity
between factors and thus implies a reduction in the efficiency of
the firm when there is uncertainty.
The total expected profit of the firm is a function of
(1) the expected prices, (2) the accumulation rates over the whole
interval 1, 2, ., n, (3) the technical and technological coef-
ficients, and (4) the amounts of the products and factors used over
the interval 1, 2, .., n'.2 The problem for the farmer is to
maximize profit through appraisal of the above factors. His plans
will change with changes in expectations. It follows that the less
certain his expectations are, the less precise his appraisal of
these factors will be, and the slower he will be in changing his
The case for crop insurance, therefore, rests in part on
the extent to which crop insurance can be used to measure the costs
of the uncertainty inherent in the weather, thus making it possible
Cf. J. R. Hicks, op. cit., p. 95, J. R. Hicks, The Theory
of Wages (London: Macmillan. and Company, Ltd., 1932), pp. 233-239
and 246-247, Joan Robinson, Economics of ImPerfect Comnetition
(New York: The Macmillan Company, 1933), pp. 256ff., and R. G. D.
Allen, Mathematical Analysis for Economists (New York: The Mac-
millan Company, 1939), Chapter XIX.
2This formulation follows 0. Tintner, "The Pure Theory of
Production Under Technological Risk and Uncertainty," Econometrica,
VIII-X (1940-41), 305-312.
for a farmer to substitute a measurable cost for one that is large-
ly uncertain, and thus allowing a more precise evaluation of the
marginal contribution of each resource. The general theoretical
outline indicates that the use of crop insurance should improve
resource utilization by minimizing the effects of increasing risk,
by reducing capital rationing, thus reducing the restrictive ef-
fects of risk aversion. The farmer may establish his scale of
enterprise nearer the point of maximum profit. Being able to de-
termine his costs more accurately, his plans should become more
responsive to changing crop prospects and market conditions. These
changes are recognized as conducive to a more efficient utilization
3. Attempts to Establish Crop Insurance Programs
Crop insurance has been attempted in every major country of
the world. Two general results have occurred. Either (1) the pro-
gram was discontinued because of large underwriting losses, or (2)
the program was continued only because the government (a) subsi-
dized it and/or (b) made it compulsory. In no case has crop in-
surance become self-supporting on a voluntary basis.
In foreign countries, crop insurance generally has taken
some form of State insurance. One explanation of this is that the
technical difficulties encountered have been too great to be han-
dled by private companies with limited resources, since crop losses
can approach the magnitude of a calamity or a national catastro-
phe. In the United States, however, all major attempts to provide
crop insurance prior to 1938 were made by commercial insurance
companies.2 The Federal Crcp Insurance Act of 1938 marked the
1See F. Arcoleo, "Crop Insurance," Intrnational Review of Ag-
riculture (Rome: International Institute of Agriculture, 1940), p. 273E.
2See J. C. Clendenin, "Federal Crop Insurance in Operation,"
Wheat Studies of the Food Research Institute, XVIII (1942), 275-277;
and Report and Recommendations of the President's Committee on Crop
insurance, House Document No. 150, 75th Congress, First Session
1937, pp. 2-3.
first attempt of the United States Government to write all-risk
Crop insurance was written for brief periods beginning in
France in 1858,1 in Finland in 1860,2 in Germany in 1870,3 and in
Denmark in 1910.4 In Sweden plans were made to insure crops but
these plans were abandoned because of expected potential losses.5
In 1888, the Japanese government hired a German economist to study
the feasibility of crop insurance. He recommended a plan for crop
insurance but the Japanese did not institute crop insurance until
1938, at which time it was made compulsory.6 The Soviet government
also has adopted compulsory crop insurance. Under a decree of
1940, field, truck, and nursery crops were insured against hail,
blizzard, storm, fire at roots, freezing, and floods.7 Compulsory
crop insurance was instituted in Switzerland in 1920.8 Unsuccess-
ful attempts were made to establish systems of non-compulsory crop
insurance in Greece in 1927 and in France during 1929 to 1937.9
Arcoleo, loc.cit. Transalted from Hemard, Theorie et
pratique des assurances terrestreS (Paris 1927), 1st part, p. 213.
2bid. Translated from Lans-Stauffer and Rommel, Elemen-
tarshaden and Versicheruno (Born 1936), Vol. 1, p. 112.
3jhid., p. 274E. Translated from Rommel, TLasstirance
centre la pelic, reprint from the Revue Generale des assurances
terrestres, No. 1, 1938.
4abi. Translated from Lans-Stauffer and Rommel, on. cit.,
Vol. 1, p. 87.
5M. Hilderbrandsson, "Insurance of Meteorlogical Risks,"
International Review of Agriculture (Romet International Institute
of Agriculture, 1924), pp. 137-138.
6See Report and Recommendations of the President's Com-
mittee on Crop Insurance, House Document No. 150, 75th Congress,
First Session 1937, p. 2.
7A. Chayanov, "Problems of Rural Insurance (U.S.S.R.)"
International Review of Agriculture (Rome: International Institute
of Agriculture, 1927). For general discussion see V. Katnoff, "How
Russia Reduces Risks of Farming," Land Policy Review, IV (1941,
8Arcoleo, op. cit., p. 274E.
Ibid., p. 309E.
In Canada, an act with certain unique provisions was
adopted to alleviate distress in the prairie provinces. This set,
known as "The Prairie Farm Assistance Act,"' imposes a tax of one
percent on elevator receipts of wheat and orders benefits paid to
farmers when wheat sells for less than 80 cents per bushel or when
widespread crop failure occurs. The act is divided into two parts,
one dealing with a state of "National Emergency" and the other with
a state of "Crop Failure."
"National Emergency" is declared by the Governor in Coun-
cil, under which there are three conditions when payments may be
made to farmers: (1) If the average price of No. 1 Northern wheat
between July 31 and November 1 is below 80 cents a bushel at Fort
William and the average yield of wheat in a township is between 8
and 12 bushels an acre, every resident farmer in the township is
paid 10 cents per acre up to half his acreage of cultivated land
for every cent, not to exceed ten, by which the price of wheat is
below 80 cents. The maximum acreage on which payments can be made
is 200; resulting in a maximum payment of $200 to any farmer. (2)
Regardless of price, if the average wheat yield in a township is
4.1 to 8 bushels per acre, a farmer is to be paid $1.50 per acre
for one-half his cultivated acreage up to 200 acres. Maximum pay-
ment would be 4300. (3) Regardless of price, if the average wheat
yield in a township is less than four bushels per acre the payment
would be $2.00 per acre, for one-half the cultivated acreage, up
to 200 acres. Maximum payment would be $400.
1For more general discussion see R. E. ibtherwell, "A
Study of Crop Insurance," Renort of the Sanketcnhean Reconstruc-
io Council,, Appendix 3 (Regina, 1944); Mknitoba Economic Survey
Board, "Crop Insurance in Manitoba: A Report on the Feasibility
and Practicability of Crop Insurance in Manitoba" (Winnipeg 1940
mimeographed); Anddrew Stewart "Crop Insurance in Alberta" fUn-
Dublished Report, Alberta Post-War Reconstruction Committee,
dmonton, 1945) Andrew Stewart, "Stabilization of the Income of
the Primary Producer," Canadian Journal of Economics and Political
Science, XI (1945), 359-372.
The "Crop Failure" clause of the Prairie Farm Assistance
Act provides that when at least 171 townships in Saskatchewan or
90 townships in Alberta or 54 townships in Manitoba have an average
wheat yield of less than five bushels per acre, and if this loss is
not due to hail, payments are made to each resident farmer in the
area at the rate of $2.50 per acre for one-half the cultivated
acreage up to 200 acres. The maximum payment to any one farmer
would be $500 with a minimum payment of $200.1
In the United States, all attempts made by commercial com-
panies to write insurance covering more than hail were short lived.
One attempt was made in 1899.2 The next was in 1917 but the com-
panies lost about $200,000 on the venture.3 In 1920 several com-
panies sold some crop insurance but one company alone lost about
1.7 million dollars.4 Again in 1930-31 and in 1937 mutual com-
panies attempted to sell crop insurance but all failed.5
The Federal Crop Insurance Act of 1938 brought to an end
all major attempts by private companies to insure crops.6 Under
this act Congress established the Federal Crop Insurance Corpora-
tion7 as the administrative agency. Insurance at first was
1Payments and receipts of farmers under the Prairie Farm
Assistance Act from 1939 to 1944 were as follows: Alberta farmers
paid $3,428,208 and received $7,653,744. The farmers of Saskat-
chewan paid $6,452,763 and received $28,999,711. Manitoba farmers
paid in $1,910,211 and received 41,530,405. The total paid by
farmers under the one percent tax was about 30 percent of their
total receipts. See Motherwell, on. cit., pp. 43 and 44.
2Congressional Digest, December 1936, p. 292.
3C. L. Rogers, "Crop Insurance," Conference Board Bulletin
(National Industrial Conference Board, New York, 1936), p. 81 and
G. Wright Hoffman, "Crop Insurance Its Recent Accomplishments
and Possibilities," AnnAls of American Academy of Political and
Social Science, CXLI (1925), 99.
4Rogers, on. cit., pp. 81-83.
information on federal crop insurance before 1942 is from
Clendenin, on. cit., pp. 229-290.
7Hereinafter sometimes abbreviated as F.C.I.C.
restricted to wheat, covering the 1939, 1940, and 1941 wheat har-
vests. In 1942 cotton insurance was added. In 1943 the Congress
terminated the crop-insurance program and no insurance was sold on
crops to be harvested in 1944 or on winter wheat for the 1945 har-
vest. From 1945 through 1947 wheat, cotton, and flax were insured
on a nation-wide basis. The 1947 amendment to the Federal Crop In-
surance Act, however, placed the entire crop-insurance program on
an experimental basis and restricted the scope of the program. The
amendment provided that, commencing with the 1948 crop, insurance
could not be offered in more than 200/counties in the case of wheat,
56 counties in cotton, 50 counties each in corn and flax, and 33
counties in tobacco.2 Insurance could not be offered in any county
unless applications filed plus contracts in force covered at least
200 farms, or one-third of the farms normally producing the com-
modity, whichever was smaller.
A financial summary of federal wheat crop insurance is pre-
sented in Table 2. A statement of the Senate Committee on Agricul-
ture and Forestry on crop insurance experience is as follows:3
The Federal crop-insurance program can best be charac-
terized as an experiment. Up to 1947, the losses incurred
in the operation of the act had consumed $90,000,000 of
the A100,000,000 of capital provided for the Federal crop
insurance in addition to current appropriations to meet
operating costs. Appropriations for the current year pro-
vided for putting the crop insurance activities on an ex-
perimental basis in order to help develop sound principles
for conducting crop-insurance programs. The 1947 crop-
insurance program for wheat showed a substantial profit
owing to the exceptionally good crop over most of the
IInformation on crop insurance during 1942 and after is
from various issues of the Apricultural Finanoe Review (Washington:
United States Department of Agriculture) and from Report of the
Manager of the Federal Crop Insurance Corporation, 1947 (Washingt-
ton: United States Department of Agriculture, 1947).
2See 80th Congress, 1st Session, Public Law 320 (S. 1326),
p. 1, Sec. 508(a).
3See 80th Congress, 2nd Session, Long-Ranae Agricultural
Policy and Program. ReOort of the Committee on Agriculture and
Forestry, United States Senate (Report No. 885, February 9, 1948),
SUMMARY OF FEDERAL WHEAT CROP INSURANCE, 1939-1946
U. S. of
Acreage Seeded U. S. Premiums Indemnities Percent of
Insurz6d Acreage Seeded Collected Paid Indemnities
(1,000 (1,000 Acreage (1,000 (1,000 Covered by
Year fares) acres) Insured bushels) bushels) Premiums
1939 7,010 62,801 11.1 6,670 10,164 65.6
1940 12,755 61,610 20.7 13,797 22,898 60.3
1941 11,734 62,332 18.8 12.643 18,857 67.0
1942 9,631 52,227 18.4 9,770 10,575 82.9
1943 8,149 55,127 14.8 8,035 13,210 60.8
1945 1,099 68,781 1.6 1,085 471 230,4
1946 9,228 71,536 12.9 9,226 5,367 171.9
Sources: APricultural Statistic, .196 (Washingtont United
States Government Printing Office), p. 7, Agricultural Finance Re-
view, IX (1946), 110; Renort of the Manlger of the Federal Crop
nsura~oe Corporation, 1947, s.. cit., p. 11 and TheWheat Sita-
io (Washington: United States Department of Agriculture, Septem-
ber-December 1947), p. 10.
The results described above have been considered by many
to be disappointing. At the same time it may be generally re-
cognized that the case for crop insurance is strong and that even-
tually some satisfactory form of crop insurance may be developed.
It is our purpose to examine the theoretical forms on which crop
insurance may be based with the thought that this analysis may be
informative to students of the subject and to those charged with
the development and administration of a crop insurance plan.
INSURANCE GUIDES APPLIED TO CROP INSURANCE
Insurance may be defined according to function as a social
device (1) which is used to measure the mathematical probability
of loss faced by the insureds of a group and (2) which distributes
the loss suffered by some of the insureds among all those in the
group. According to legal definition, insurance is a contract in
which the insurer or the insurance carrier agrees to make good any
financial loss an insured may suffer within the scope of the con-
tract in consideration of the premium paid by the insured. Certain
guides or rules, sometimes listed as essential requirements for
successful insurance practice, have attained general acceptance
among commercial insurance companies. It seems desirable to state
these guides or rules and to examine their economic and mathemati-
cal content in order to determine how they apply in the theory of
crop insurance. This examination may help (1) to outline the
framework within which crop insurance should be written and (2) to
suggest means for dealing with the problems which are peculiar to
Some of the guildes which have been accepted are as fol-
lows:1 (1) The insured should have an insurable interest in the
object insured; and the insurable interest should be such that it
will exist independent, or will not be affected by action, of the
For further discussion see Robert Riegel and Jerome S.
Miller, Insurance PrinciDles and Practices, 3rd ed. (New York:
Prentice-Hall Inc., 1947), Chapter II. See also John H. Magee',
General Insurance, 3rd ed. (Chicago: Richard D. Irwin, Inc.,
1947), Chapter IV; Francis T. Allen, General Principles of In-
surance (New York: Longmans, Green and Co., 1941), Chapter II.
party insured. (2) The risk to be insured must be important enough
to warrant the existence of an insurance contract. (3) The cost of
insurance must not be prohibitive. (4) A large number of risks is
necessary. (5) The probabilities of indemnity must be capable of
estimation in a mathematical sense.
1. The Insuranble Interest
It has been stated that "a person has an insurable interest
in the object insured whenever he may suffer direct and immediate
loss by the destruction or injury of it."l In property insurance,
the doctrine of insurable interest rests on the principle that in-
surance is intended for indemnity, for making good a loss, and not
for gain. The doctrine is justified for two reason, which are:
(1) to insure a person without an insurable interest is pure gam-
bling, and it should not be public interest to assist in the col-
lection of gambling gains; and (2) without insurable interest a
person would be encouraged to bring about the very contingency
The nature of the insurable interest may be defined in the
policy. In most insurance policies covering an interest in pro-
perty the insurable interest is carefully described with the object
of determining the insurer's liability under specific conditions.
Provisions are attached to exclude liability under certain contin-
gencies.2 The insured, therefore, may not be covered against any
and all possible contingencies. Thus the usual property insurance
policy defines the insurable interest and indicates what specific
risks are covered.
1Allen, ibid. p. 9. The quotation is found in the Civil
Code of Lower Canada.
2An example of coverages and of contingency provisions may
be found, for example, in the section of the New York Standard Fire
Policy relating to "extent of participation." In 1947 this policy
was in use in 40 states in the United States. See Riegel and
miller, on. cit., pp. 352ff.
The extent of the insurable interest is generally deter-
mined by the amount of loss that will be suffered by the insured
if the event or contingency insured against actually occurs. MYst
insurance policies, however, do not cover the full insurable in-
terest.1 In cases where a total loss occurs and it is found that
the face value of the policy exceeds the insurable interest the
indemnity is measured by the actual loss sustained.2 In case of
most property insurance the insurable interest must exist at time
Standard concepts of insurable interest must be modified,
however, when consideration is given to the problem of insuring
crops. A farmer's insurable interest in a crop may be defined
(1) as the discounted value of a potential yield, or (2) as the
investment in a growing crop. In most systems of crop insurance
the insurable interestt has been defined as an interest in all or
part of a potential yield4 and indemnities have been calculated
(1) on the basis of estimated damage to the yield, as in case of
hail insurance, or (2) on the basis of a deficiency from some in-
sured level of yield, as in the case of the all-risk insurance de-
fined above. In some other instances the insurable interest of
the farmer has been defined as his investment in the growing crop.5
2However, when valued policies are used, in which case the
insurable interest is previously established on basis of values
mutually agreed upon, they have the effect of making the agreed
valuation binding upon both the insured and the insurer. See
Magee, on. cit., pp. 270 and 434.
3kbid., p. 434
4See Rogers, on. cit., pp. 81-83, Conrepssional Dieest,
loc. cit., and Clendenin, on. cit., pp. 275-281.
5Clendenin, ibid., pp. 275 and 276. In instances before
1938 the insurance carriers experienced losses (1) because of in-
accuracies in farmers' reported costs, and (2) because price de-
clines as well as poor crops were important causes for indemnities.
Investment insurance has been sold on an experimental basis by the
F.C.I.C. for tobacco and corn. See Report of the Manager of the
Federal Cron Insurance Corporation, 1947, on. cit., pp. 25,30.
In some other cases attempts have been made to reduce the carrier's
liability by restricting the yield coverage to a level not ex-
ceeding the average investment in the crop at time of abandonment
of the crop.
The farmer's insurable interest, by either of the above
definitions, comes into existence by stages. The actual extent of
the insurable interest at any one time is dependent, in part, on
yield and price expectations. Consequently wide variations in in-
surable interest are possible, and perhaps probable; and events may
be of such adverse character that loss may be evident before the
major part of the insurable interest comes into existence. The
insurer may be placed in the peculiar position of insuring some
interest which never actually comes into being and yet if the in-
demnity is placed in default the farmer will suffer because all
source of crop income may be eliminated for an entire year. The
usual concept of insurable interest may have to be modified, there-
fore, in order (1) to provide the farmer with an adequate means of
protection against adverse crop conditions and (2) to protect the
insurance carrier in a case of writing a policy which covers an
interest that may not exist at a time when loss occurs.2
1The F.C.I.C. was required in the 1947 amendment to the
Federal Crop Insurance Act to limit coverage to 75 percent of
average yield on the insured farm provided this coverage should
not exceed the average investment in the crop in the area. See
80th Congress, 1st Session, Public Law 320 (S. 1326), p. 1, Sec.
508(a). In two earlier instances when insurable interest was
limited the volume of insurance coverage declined sharply and the
companies selling the insurance experienced losses. See Clendenin,
ibid., p. 276 or Rogers, op. cit., p. 83.
2Crop insurance may be likened to rain insurance which
covers such things as band concerts, football games, carnivals,
fairs, circuses, etc., because the most widely used form of rain
insurance is intended to insure events with an income expectancy
rather than a property with a definite insurable interest. A
special set of rules must be developed to state the time and con-
ditions under which an indemnity may be paid. See Magee, op. cit.,
Yield expectations are influenced by farming methods and
by investments in the crop. Furthermore, crop investments are in-
fluenced by price and market expectations as well as by yield ex-
pectations. Actuarially speaking, however, the probability of
indemnity must not be influenced by action of the insured if ad-
verse selectivity is to be avoided.
In this dissertation we approach the problem of insurable
interest as follows:
In the case of all-risk crop insurance the insured yield
is usually placed at such a low level it may be assumed that any
action of the farmer which is within provisions of the policy will
not reduce the insurable interest to a level below the insured
yield. In other words, it may be assumed that the action of the
farmer may affect Lis insurable interest but not sufficiently to
reduce the potential value of the crop to something less than the
insured yield. We shall examine this assumption in the next chap-
ter in an attempt to determine under what conditions, if any, the
farmer may voluntarily reduce his investment in the crop and/or
the potential value of the crop to something less than the value
of the insured yield.' We shall attempt to determine also what
the relationship between insurable interest and insured yield may
have to do with the inclination to insure.
In the case of area-yield insurance, the individual far-
mer's insurable interest, as previously defined, is dealt with by
assuming that there is a positive and highly significant correla-
ation between the area yield and the crop condition faced by an
individual farmer in the area.2 If this assumption is valid, the
1Clendenin concluded that low yields on insured crops were
seldom the result of willful mismanagement. See J, C. Clendenin,
"Crop Insurance An Experiment in Farm Income Stabilization,"
Journal of Land and Public Utility Economics, XVI (1940), 277.
2This assumption is reviewed in Chapter V.
crop condition faced by the farmer can be insured by insuring area
yield. Since a farmer's yields will depend on crop conditions ex-
perienced, his insurable interest in the crop can be insured by
insuring area yield.1 The probability of indemnity will not be
influenced by his action because any influence he exerts on his
own yields will have but little effect on area yields. To prevent
a farmer from over-insuring, and from thus putting himself in posi-
tion to benefit from an adverse crop condition, various limitations
are considered as to the amount of insurance he may be able to
In the case of weather-crop insurance, it is assumed that
weather phenomena influence crop conditions and yields and that the
farmer's yield, or insurable interest, may be protected by basing
premiums and indemnities on weather phenomena. In this case a
premium would be baesd upon the probability of indemnity when pay-
ment of indemnity is contingent upon the occurrence of adverse
weather. The probability of indemnity on any particular coverage
would be completely independent of the farmer's action. To prevent
a farmer from over-insuring, various limitations are considered as
to the amount of insurance he may be eligible to purchase.
2. The Imnortance of the Risk
The importance of the risk of crop loss varies widely among
areas, among crops, and among different kinds of cropping systems.
As we indicated in Chapter II, the risk may be generally recognized
but the degree of its importance in various areas and among various
crops and cropping systems must be based upon the analysis of
1This may be true providing the area is delineated as sug-
gested in Chapter V, The farmer's insurable interest is covered
only as his yields are correlated with crop conditions in the area.
It is the crop condition that is really insured therefore, Cf.
Magee, pn. cit., Chapters XIV, XV, XXXI, and Francis T. Allen,
op.&_i.., Chapter XIII.
3. The Cost of Crop Insurance
The third rule or guide stated above is that the cost of
insurance must not be prohibitive. We may assume, as a first ap-
proximation, that two things may cause costs to be prohibitive
(1) administrative expenses, covered by the loading in the premium,
may be so high as to discourage the use of insurance, and/or (2)
actuarial procedures may be such that the part of the premium set
aside to pay indemnities may be greater than the farmer's estimate
of his loss probability. The first cause might be eliminated (a)
by having the insurance carrier assume the costs of administra-
tion,1 or (b) by obtaining a large number of risks and by efficient
organization and operation of the underwriter's business. The
second cause might be eliminated, as a first approximation, by
correcting actuarial procedure.
The second cause of prohibitive costs cited above may have
been the most important cause of failure in past attempts to write
crop insurance. In a survey conducted among farmers who were not
using crop insurance offered by the Federal Crop Insurance Corpora-
tion, for instance, the following reasons were given for not buying
"I tried insurance twice, and paid in $500 and got nothing
back. I can't continue such losses."
"Premiums are too high."
"They raised my premiums because other people had losses."
"I earned lower premiums by raising good crops, without
any losses, but they raised my premiums anyhow."
"The insured yield is erroneously low."
1As is done in case of the crop insurance sold by the
Federal Crop Insurance Corporation and in case of the National
Service Life Insurance Policies.
2See Clendenin, "Federal Crop Insurance in Operation,"
on. cit., p. 258. Clendenin cited the reasons as being typical.
"The policy won't cover the loss if a portion of a bumper
crop is destroyed, so hail (and other) insurance is needed whenever
the crop looks promising. It is therefore better to buy these
other forms and take a chance on uninsured losses."
"The policy does not cover all legitimate losses."
"Prethreshing adjustments are unsatisfactory."
These statement indicate that the general dissatisfaction
occurred because premiums were higher than the individual farmer's
estimate of the discounted value of potential losses.1 Even if
actuarial procedures are correct, however, farmers in some areas
may prefer the chance of a large uncertain gain to one that is
smaller and more certain. This may be true especially in a high-
risk area, when the use of insurance may commit a farmer to a fair-
ly definite level of income which he may consider undesirable.
Without insurance he has a possibility of a higher income as well
as a lower income, Such a farmer might not have a positive liking
for danger but he might have a lower preference functional for cer-
tainty than would some other farmers, e.g., those in a low-risk
1In another investigation it was concluded that participa-
tion was influenced by the previous year's crop with "a poor
crop tending to increase insurance in the following year .
good crop prospects tending to decrease participation." See Sum-
mary of Report of the Wheat Crop Insurance Consultina Committee on
the Operations of the Federal Crop Insurance Corporation, by R. J.
Laubengayer, W. G. Cochran, H. L. Ekern, Chairman (1942), p. 27.
2Tintner has pointed out that "different individuals will
have different preferences for high or low probabilities, according
to the question if they are more or less gamblers. A gambler, for
instance, will prefer long odds, this is to say, a large gain even
if connected with a low probability. This introduces the property
of the skewness of the probability distribution .. We can as-
sume that there is for every individual a preference function or
rather preference functional which will depend on the probability
distribution mentioned." See Gerhard Tintner, '"A Contribution to
the Non-static Theory of Production," Studies in Mathematical Eco-
nomics and Econometrics, Lange, et. al., ed. (Chicago: The Univer-
sity of Chicago Press, 1942), p. 107.
Another possibility that may cause a cost to seem prohibi-
tive, in case of all-risk crop insurance, is that a farmer may be
optimistic about his yields. The more optimistic he is the more
odious a given premium rate would be.
Neither of these last two possibilities, however, disprove
the postulate that in general costs will be prohibitive only when
they are inconsistent with the loss probabilities faced by the in-
dividual farmer,2 assuming that most individuals have a distaste
for danger or at least are neutral to it.3
4. The Number of Risks
The fourth rule of insurance given above is that a large
number of risks or insureds is necessary. This is necessary be-
cause (1) a large number of risks reduces the average administra-
tion expense per contract and (2) the probability distribution of
losses may be estimated with increasing accuracy as larger numbers
of risks are included, in accordance with the theory of large num-
bers. These rules find an application in crop insurance.
Administrative expense is a matter for empirical rather
than theoretical verification. We may merely illustrate how ex-
penses have been correlated with the number of risks in case of
the all-risk insurance. Operating expenses per premium bushel and
per protected bushel declined as a larger percentage of total
IThis possibility may carry little weight in the case of
area-yield insurance and no weight in the case of weather-crop
insurance. See below Chapters V and VI.
2Hart has shown that devices for meeting uncertainty do
not necessarily lower profit expectations. See A. G. Hart, "Risk,
Uncertainty, and the Unprofitability of Compounding Probabilities,"
Lange, et al, ed., op. cit., pp. 110-118. Crop insurance may, in
fact, improve profit expectations in an essentially risk situation
by eliminating forced liquidations caused by a run of poor crop
years, the case of risk being applied to any crop yield proba-
bility, or to any crop condition probability, in any year.
3Hart, ibid,, n. p. 116.
acreage was insured. The average cost per bushel was about two-
thirds as high where 40 percent of total acreage was insured as
it was where 17.8 percent was insured (see Table 3).
TYPICAL OPERATING EXPENSES OF THE FEDERAL CROP
INSURANCE CORPORATION UNIER CONDITIONS ASSUMED
Assumed percentage of
AREA 17.8 t 30.0 k40.0 i 17.8 30.0 40.0
Operating expenses Operating expenses
.____..__. per premium bushel I per protected bushel..
United States average $.33 $..4 $.21 $.031 $.023 $.020
Ohio Valley state .67 .49 .42 .036 .026 .022
Northern state .55 .40 .35 .041 .030 .026
Western Great Plains a~ea .22 .16 .14 .038 .028 .023
Pacific Coast state .33 .24 .21 .019 .014 .12
Source: C. L. Clendenin, "Federal Crop Insurance in
Operation," Wheat Studies of the Food Research Institute, XVIII
With crop insurance in the United States, the probability
that the aggregate indemnities will approach the aggregate premiums
in any one year should increase as uniformity is achieved in the
distribution of risks geographically and among crops. This is true
because agricultural production of crops over the nation tends to
be more stable than the crop production in any one area or than the
production of any one crop.1 Although there will be a tendency for
aggregate or total losses to become more predictable as the numbers
Total agricultural production did not fall off as much as
10 percent during the unprecedented drouth of 1934 and 1936. See
T. W. Schultz, Agriculture in an Unstable Economy, on. nit., p. 10.
Total crop production is less stable, however. The index of crop
production per acre (with 1935-39 = 100) went to 73 in 1934 and to
126 in 1942. See Sherman E. Johnson, op. cit., p. 67. Individual
crop production is still less stable. Corn production, for example,
was about 1.5 billion bushels in 1934 compared with 3.2 in 1944;
Agricultural Statistics. 1946, o, cit., p. 39.
of farms, geographic areas, and crops covered by insurance in-
crease, generally poor weather over the Nation, as in 1934 or 1936,
could make an indemnity probable on an unusually large number of
policies. Likewise favorable weather, as in 1942, 1945 or 1946,1
could reduce indemnities below premiums for the country as a while.
In the case of crop insurance large numbers are necessary to re-
duce unit administrative costs and to improve the distribution of
losses; but large numbers alone will not guarantee that losses will
be equal to indemnities in any one year.
5. The Mathematical Calculation of Risks
The fifth rule of insurance given above is that the extent
of the hazard involved must be capable of mathematical estimation
or calculation.2 (1) The probability of loss must be known, with
some degree of certainty, for the statistical universe and (2) the
individual risks, or the insureds, must be classified so that a
Favorable weather is recognized as only one of the factors
bringing about increased production in the above years. Sherman
Johnson stated that, "Considering the average of the years 1942-44,
it appears that no more than one-fourth of the total increase in
production can be accounted for by weather conditions that were
more favorable than in the prewar years 1935-39. This means that
with normal weather the gross farm production in 1942-44 would have
averaged about 117 percent of 1935-39, and farm output would have
averaged at least 120 percent .. Obviously then, only a rather
small part of the wartime increase in production can be explained
by the extremely favorable weather .. Agriculture has ex-
perienced a production revolution during the war years. And a
large part of the change is irreversible." Quoted from Sherman
E. Johnson, op. cit., p. 2.
2There may be an exception to this rule in cases where
there are peculiar circumstances, or few data. In such cases the
question of probability is not readily subjected to statistical
treatment and rates are dependent upon degrees of belief registered
in the minds of the interested parties. Probability is entirely
subjective in such cases and it may be at variance with existing
fact. For example, in days before swift steamships and radio com-
munication the insurance of overdue ships "lost or not lost" was
a common practice. Bits of information on weather, on condition
of the vessel before sailing, on the kind of cargo, etc., would
have the effect of raising or lowering rates. Rates might vary
from day to day. None of the information could alter the fact
that at time of negotiating the premium the ship was either sunk
or afloat. Cf. Magee, on. cit., pp. 218-229.
common premium rate will apply to all risks with similar proba-
bilities for indemnities. The first condition must be established
in order that the insurance carrier may be able (a) to estimate
reserves required to meet indemnities, and (b) to establish premium
rates sufficient to build up these reserves, to meet losses and the
costs of doing business. The second condition must be established
so that costs may be equitable between the different classes of
risks and so that an adverse selectivity may not develop among
those eligible for insurance.
The probability of loss in the statistical universe varies
with the definition of the universe. The universe might be defined
as all the farms in a type-of-farming area,1 in a county, in a
state, or (say) in the entire United States.
In whatever manner the universe is defined, the variations
in crop conditions experienced would tend to make aggregate pre-
miums for the universe different from aggregate indemnities in any
one year. The carrier writing crop insurance, therefore, might
find it necessary to carry a high reserve ratio compared with re-
serve ratios carried by a life insurance company or an automobile
insurance company. The probabilities of loss in crop insurance
might be measured as accurately over a period of 10 or 15 years,
however, as in the case of life or automobile insurance.
The more difficult question in crop insurance, perhaps,
revolves around the concept of how risks may be classified so that
a common premium rate will apply to all risks with similar loss
probabilities. The problem of insuring crop yields presents ser-
veral peculiarities. (1) Farms are not easily classified according
to yield probabilities. Even if past yields on an individual farm
are accurate and give a true picture of productivity in past years,
1See below, Chapter V, part 1.
changes in management practices, changes in farm technology or in
seed, etc., may raise or lower the mathematical expectation of
yields on an individual farm. (2) Low yields or adverse crop con-
ditions, whichever are a cause for indemnity payments, do not occur
necessarily in any "normal" pattern geographically.1 (3) A poor
crop, which can be experienced frequently, may cause the farmer
as much loss as a complete crop failure, because the cost of har-
vesting a poor crop, plus the loss necessitated by the delay in
seedbed preparations for the next crop,2 may approach the value
of the crop. Therefore, if crop insurance is to offer protection
to the farmer under all conditions in which loss can occur because
of adverse crop conditions or low yields, the indemnities might
need to be as large for a wheat crop of (say) five bushels, or for
moderately bad crop conditions, as for a complete crop failure.
The scale of indemnities should, perhaps, increase rapidly below
some insured level to reach a maximum at the level of a poor crop
and to retain this maximum through the stage of complete crop
failure. In such a case indemnities might be large and of frequent
occurrence. (4) Loss through low yields or adverse crop conditions
is a matter of degree and indemnities are not dependent on the oc-
currence of a single event.
1Von Neumann and Mirgenstern pointed out that in utilizing
a group of physical variables to maximize satisfaction "sometimes
uncontrollable factors also intervene, e.g., the weather in agri-
culture. These, however, are purely statistical phenomena. Con-
sequently they can be eliminated by the known procedures of the
calculus of probabilities: i.e., by determining the probabilities
of the various alternatives and by introduction of the notion of
'mathematical expectation' .." See John von Neumann and Oskar
Mbrgenstern, Theory of Games and Economic Behavior (Princeton;
Princeton University Press, 1944), p. 10. We add that this notion
of mathematical expectation may apply to crop yields over a series
of years but the mean yield expectation must change as new condi-
tions, such as new varieties, improved techniques, etc., are an-
ticipated or are realized,
2Cf. T. A. Kiesselbach, Arthur Anderson, and W. W. Burr,
The Seedbed Factor in Winter Wheat Production, Nebraska Agricul-
tural Experiment Station Bulletin 228 (1927).
The solution for crop insurance must be based (1) on the
recognition that such peculiarities do exist and (2) on a defini-
tion of what we wish crop insurance to accomplish. We take the
position that crop insurance should be designed to insure against
losses which can be attributed to adverse weather and to disease
or insects associated with adverse weather. The function should
be to insure the physical crop conditions faced by the farmer.
We have seen that some other types of insurance, such as fire and
casualty, are of this type; insurance is provided to protect the
insured against losses which can be attributed to the occurrence
of certain specific events. Crop insurance should not be designed
to protect a farmer against losses which may be caused by his
management practices. The problem, therefore, is chiefly (1) to
develop a means for measuring the crop losses attributable to ad-
verse physical crop conditions and (2) to calculate the correct
premium rates to apply to each class or type of risk. The problem
may be visualized and the solution may be indicated by developing
the relevant theory applicable to alternative plans. This task is
undertaken in the three chapters following.
CROP INSURANCE BASED ON INDIVIDUAL FARM YIELDS
An example of crop insurance based on individual farm
yields is offered by the all-risk crop insurance which was used
in the United States during 1939-43 and which has been continued
since 1945. This chapter states the theoretical premises on which
this insurance might be based andundertakes to determine whether
such insurance can work successfully, according to standards
1. The General Theory and Assumptions
When all-risk crop insurance was begun in the United States
it was assumed that an individual premium rate would be established
for each farm. It was assumed that this rate would be based on the
average yields experienced on that farm during a representative
base period and that the premium rate would be used to insure a
given percentage of the base yield. Two options were offered:
one insuring for 50 percent of the base yield, and the other in-
suring for 75 percent of the base yield. It was assumed, ap-
parently, that setting the insured yield at a fraction of average
yield would eliminate most of the adverse effects which might be
associated with certain errors in recording yields. It is our pur-
pose now to determine under what conditions and assumptions such
a program could work successfully.
The theoretical problem can be simplified by making the
following assumptions: (1) There are in a given county a group of
farmers, (a) who grow only one crop, and (b) who plant the same
acreage of crops each year. (2) All the farmers in the county who
purchase insurance accept a long-term contract to cover (say) 75
percent of their base yield. (3) The average yields on each of
the farms in the base period are the same as the county yield in
the base period. (4) All farming practices, technical and techno-
logical conditions, remain the same on each farm as they were
during the base period.
In the analysis which follows the above assumptions are
dropped one at a time in reverse order. One other assumption must
be tacit throughout. It is that a farmer has a fairly accurate
idea of his own yield potentiality with a given kind or type of
weather. Since the weather is unpredictable for a season in ad-
vance, however, he does not know what the average yield will be
for his own farm or for the other farms in the area. It is as-
sumed also that each farmer has knowledge of soil and moisture
conditions at planting time and therefore has some knowledge of
the yield he will receive on a given piece of land compared with
yields on other fields on his own farm, and that each farmer has
some knowledge of how his yields will compare with those of his
neighbors. This latter group of assumptions appears to conform
with general observation.
All Basic Assumptions Fulfilled
If all the assumptions outlined above are retained, in-
demnities would be equal to premiums over any long period of time.
Whether insurance would maximize the discounted value of a farmer's
returns depends on the sequence and timing of the indemnity pay-
ments. It is assumed that the pattern of indemnity will be random.
Whether a farmer would prefer to be insured or not depends on the
assumption made concerning his attitude toward uncertainty, on his
capital position, and on the degree of variation he expects in
yield. Considering the general conditions of increasing riskI
and capital rationing which we find in agriculture, it may be con-
cluded that insurance under conditions assumed would be generally
acceptable.2 The actual degree of acceptability, however, must be
judged from actual experience rather than from a prior reasoning.
Technical and Technological Conditions Change
Assuming that technical and technological conditions
change, the most realistic assumption covering the United States
seems to be that the trend of yields is upward on some farms and
downward on others and that the upward trend is more pronounced.
Agricultural output has increased.3 Yields have increased in
varying degrees and further yield increases are in prospect for
the majority of farms.4 Since this assumption of changing yields
is basic, it is considered in some detail.
"Experience with hybrid seed corn indicates that acre
yields are increased about 20 percent over the yields of open-
pollinated varieties. The percentage increase is usually about
the same on good as on poor land .."
1The principle of increasing risk applies generally, even
where the farmer has no fixed interest-bearing obligations, if
capital rationing, either external or internal, exists. The entre-
preneur should be indifferent to increasing risk only if he has an
unlimited capital budget. Such a situation is seldom found in
2Cf. Hart, "Risk, Uncertainty, and the Unprofitability of
Compounding Probabilities," op. cit., n. p. 116 and F. H. Knight,
on. cit., p. 46.
3"The over-all production of agriculture increased about
60% from 1910 to 1945, while the production per worker increased
almost 100% .." See the report of the Special Committee of the
House of Representatives on Postwar Economic Policy and Planning
(sometimes referred to as the Colmer Committee), 1946 Report on
Postwar Apricultural Policies (79th Congress, 2nd Session, House
Report No. 2728).
4The following data on yields are from Sherman E. Johnson,
n. cit., pp. 26-36, except where otherwise noted.
In the case of soybeans ". The trend in yield has been
upward New varieties of soybeans, especially the Lincoln,
give promise of further increases in yield per acre within the next
few years .." In case of some other crops, such as hay, yields
have been increased by shifting to a different species. ". A
crop change that developed gradually over the interwar and war
years was the shift in hay acreage from grasses to the higher
yielding legume hays ..." The trend in the grain sorghums is
not clear because ". .. The grain sorghums are grown largely in
the Great Plains States where the yields vary over a wide range,
depending on weather .. .." Yields of some of the feed grains
have been increased by the introduction of new varieties. For in-
stance, ". New varieties of oats have been introduced that
result in increases comparable to those of hybrid corn in yields
per acre .." Some new varieties of barley have yielded from
20 to 30 percent more than the older varieties.1
Wheat yields have been increased. ". Wheat production
averaged more than one-fourth higher in 1942-44 than in 1935-39,
with a planted acreage only four-fifths as large Back of this
increase are improved varieties, soil and moisture-conserving prac-
tices, and mechanization which increases the timeliness of opera-
"The continued increase in yields of cotton can be attri-
buted largely to the following factors: (1) increased use of fer-
tilizer, (2) a shift to higher yielding areas with reduction in
acreage, (3) careful selection of land within each area End on
1Two new varieties of barley, Compana and Glacier, de-
veloped cooperatively by the Mbntana Agricultural Experiment Sta-
tion and the United States Department of Agriculture, have consis-
tently outyielded older varieties. See S. G. Litzenberger, ,C1oana
and Glacier Barley, Mntana Agricultural Experiment Station Bulle-
tin, 422 (Bozeman, Montana, 1944), pp. 7-11.
individual farms, (4) use of improved varieties, and (5) increased
use of legumes ."
"There are two principal reasons for the higher yields of
potatoes. Adoption of a whole group of improved practices is one
-- raising higher yielding varieties, heavier fertilization, and
more effective insect and disease control. The second reason is
that these improvements, combined with mechanization, have pushed
more of the production into the hands of specialized commercial
growers who use the new methods on large acreages, in areas that
are especially adapted to potatoes .."
"Yields of all fruits on a bearing-acreage basis have in-
creased within 15 years. The increasing average age of the trees
probably has been the most influential single cause ..
In view of the above information, assuming that yield con-
ditions change on individual farms, it can be shown that the far-
mers with increasing yields would find that the flat premium rate
would make the sum of premiums for 15 br 20 years more than the
sum of the indemnities. The farmers with decreasing yields would
find that the flat premium rate would make the sum of premiums for
15 or 20 years less than the sum of the indemnities.
One method which might be proposed to compensate for
changes in yields on individual farms would be to use a moving
average as a base for establishing the insured yield.1 This would
tend to reduce the inequities inherent in upward or downward trends
but it would not eliminate them because of the "lag" inherent in
the use of a moving average. Insured yields would be below average
after a period of poor crop years and above average after a series
of good years. These yields would not bear any necessary
This method was proposed by T. J. Reed, See T. J. Reed,
"Crop Insurance to Stabilize Wheat Growers' Incomes," unpublished
M.S. Thesis, Iowa State College, Ames, Iowa, 1947.
relationship to expected yields.1 Because of lags inherent in most
other premium reduction schemes the farmer with increasing yields
would still find himself at a relative disadvantage in the use of
all-risk crop insurance.2
Base Yields for Farms and County Are Not the Same
Average farm yields within a county may vary widely (see
Table 4). Under such conditions, two different plans for all-risk
crop insurance might be tried. Either (1) individual farm records
might be used to establish a base yield for each farm, or (2) pre-
mium rates might be based on the county average, in which case
premium rates would be the same for all farms regardless of the
individual yield record (see Table 5). The F.C.I.C. started opera-
tions under the first plan and shifted to the second:
Early in the crop insurance program an individual
premium rate and an insured production was determined for
each farm. It has since been recognized that past yields
for individual farms are not available for a long enough
period to permit determination of an accurate farm rate
from the variations in yields, though perhaps they are
adequate to provide a fairly reliable indication of the
"expected" yield in the year of insurance. As the rates
could not equitably be determined from past yield records
the trend has been toward the use of a more or less "flat"
rate for each county, but with an individual insured
In many counties in ~bntana, the Dakotas, Nebraska, and
Kansas poor crops were experienced in 1940 and in 1941. The
F.C.I.C. raised premium rates and cut insured yields on the basis
of this experience at the same time that prospects appeared good
for 1942. As a result participation declined sharply. See
Clendenin, "Federal Crop Insurance in Operation," on. cit., p. 261.
2Two alternative "experience-rating" or premium reduction
plans were offered by the Federal Crop Insurance Corporation in
1946. (1) When a farmer had a balance of premiums over indemnities
in favor of the Corporation which equaled or exceeded his insured
production for the current year he could obtain a 50 percent re-
duction in his current premium rate. (2) When a farmer had five
consecutive years without indemnity excluding 1944 when no in-
surance was offered, he could receive a ten percent reduction in
his current premium rate. A wheat or cotton farmer carrying in-
surance could select either one of these plans in 1946, but the
plans were restricted to wheat in 1947. See Aaricultural Finance
Review. IX (1946), 72.
production for each farm. With the adoption of county pre-
mium rates for cotton in 1946, all crops in both the per-
manent and trial programs usually are insured under uniform
county-wide rates. Higher rates are charged on certain
"high risk" farms in a county.1
CLASSIFICATION OF 1269 FARMS IN CHOUTEAU COUNTY, MONTANA,
ACCORDING TO AVERAGE WHEAT YIELDS 1925-1932
Average Yield Bushels
- 2.5 .
- 5.0 .
- 10.0 .
- 12.5 .
- 15.0 .
- 17.5 .
- 20.0 .
- 22.5 .
- 25.0 .
Source: Data taken from records in
office at Fort Benton, Montana.
Chouteau County P.M.A.
COUNTY PREMIUM RATE, AVERAGE BASE YIELDS AND
AVERAGE INSURED YIELDS, IN CHOUTEAU COUNTY,
MONTANA, FOR 1947, IN BUSHELS PER ACRE
WINTER WHEAT .SRINU WHEAT
Summer Continuous i Summer ; Continuous
Fallow Crop Fallow Crop
For 75% of base yield
Average base yield
Average insured yield
For 50% of base yield
Average base yield
Average insured yield
Source: Data obtained from records in Chouteau County
P.M.A. office at Fort Benton, Montana.
Agricultural Finance Review, IX (1946), 71. Underlining
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. .. .
.e .. .
. .. .
o e .
If insurance premiums and indemnities could be based on
individual farm records (as in the first plan above) the difference
in average yields would not present any theoretical inconsistency.
If premium rates are based on county averages (as in the second
plan) and insured yields are set at 75 percent (or 50 percent) of
the average yield of the individual farms then either one of two
general situations may develop: (1) If the deviation of yields in
bushels is the same for all farms, the farmers with low average
yields would receive indemnities more often and in larger amounts
than the farmers with higher yields.1 (2) If the deviations of
yields in terms of percentage of the mean yield is the same for all
farms, the farmers with high average yields would receive larger
indemnities than the farmers with low average yields.2
Allowing for variations of different degrees, the above
situations may present an unlimited number of combinations. In
1This may be demonstrated: Let Ra = mean yield of farm A,
let Xb = mean yield of farm B, and Xn = mean yield of farm
N. Then, assuming that 75 percent of the mean yield is insured,
3/4Xa, 3/4 Xb, and 3/4Xn are respective insured yields. Let
the average variation in yields in respective years be represented
by Yl, Y2, .* Yn for years i, 2, .. n.
For example suppose: y- = + 5,y2 =- 4, Y3 = 6,
7, and y5 = + 12; Xa = 12, b = 16; 3/4Xa = 9, and 3/4Xb = 12. In-
demnities would be as follows:
Farm A = 0 + 1 + 3 + 4 + 0 = 8 bushels per acre for the
Farm B = 0 + 0 + 2 + 3 + 0 = 5 bushels per acre for the
2This may be demonstrated (as in previous footnote): Let
Xa, Xb, .and Xn be mean yields; let 3/'4Xa, 3/4Xb, and
3/45Xn be respective insured yields; and let the variation in yields
be yl (Xa), yl (kb), y(Xn); y2 (Xa),_y (Xb), y3
(Xn); and yn (Xa) yn. yn (Xn .
For example suppose where Xa = 12 and Xb = 16 that yl = +
40%, y = -40%, Y3 = + 60%, y4 = 60%, y5 = 0. Indemnities
would Le as follows:
Farm A = 0 + 1.8 + 0 + 4.2 + 0 = 6.0 bushels per acre for
the 5 years.
Farm B = 0 + 2.4 + 0 + 5.6 + 0 = 8.0 bushels per acre for
the 5 years.
order for there to be no inherent incentive for an adverse selec-
tivity the indemnity for each class of farms, ranked according to
yield, would have to be equal, at least potentially, for the entire
universe of farms which were eligible for a common premium rate.l
The fulfillment of this latter condition would appear to be highly
improbable. It should be recognized, however, that there may be
a tendency toward the fulfillment of the condition even though the
relationship might be termed highly haphazard. If the standard
deviation of yields is higher on high yielding farms than on low
yielding farms, and if the coefficient of variation is greater on
the low yielding farms than on the high yielding farms, there would
be a tendency toward the fulfillment of the above condition. There
is some evidence that such a tendency does exist.2
All Farmers Do Not Purchase Insurance
If all farmers do not purchase crop insurance, two situa-
tions may develop: (1) Some farmers may decide that the mathe-
matical probabilities of loss are not great enough on their farm
to make it desirable for them to insure and they will adopt the
policy of not insuring. (2) Some farmers may purchase crop in-
surance in some years but not in others. The first situation could
be due to the conditions outlined above for which the only solution
would be a change in actuarial procedure. The second situation
might be corrected in part by writing only a long-term contract
1Given a number of farms A, B, N, deviations of
yields on these farms, in years of indemnity, would have to be
- 1/4Xa, 1/4Xb, 1/4Xn minus some constant x which would
be the same for each farm.
2The data below are from a study conducted at 14 experi-
ment stations in the Northern Great Plains during the years 1906-
1935 and the data refer to yields per acre of spring wheat:
Eight high yielding stations: A = 16.87 = 10.83
C.V. = 64.2%
Five low yielding stations: X = 11.89 6d = 8.89
C.V. = 74.8%
See John S. Cole, op. cit., pp. 26-28.
for (say) three, five, or more years, and by setting the deadline
for purchase far enough ahead' of seeding so that estimates cannot
be accurately made of crop prospects for the next year.1
If dates of application and/or cancellation were far enough
ahead of seeding dates, the adverse aspects of year-to-year selec-
tivity should be greatly reduced. One of the difficulties with
setting the deadlines far enough ahead is that farmers may some-
times have a good idea of what yields will be even as much as a
year or more ahead of the seeding date. The writer had this ex-
perience in the period 1931 to 1936 during a severe grasshopper
infestation when it seemed that rainfall would have to be well
above average in order to obtain an average yield. Under such con-
ditions farmers would tend to insure regardless of the date for
application. It seems likely, also, that if the yields for these
years were used as a basis for determining premiums and base yields,
the use of insurance would be discouraged during other periods.2
In facing this situation the insurance carrier may choose among
several alternatives, three of which are: (1) to offer crop in-
surance at rates which disregard the additional hazard, (2) to es-
tablish premium rates at an average level which is high enough to
compensate for occasional losses by insects and/or disease; or (3)
to raise premium rates at specific times when the additional hazard
1Early deadlines have been recommended elsewhere. For
example see Clendenin, "Federal Crop Insurance in Operation,"
op. cit., pp. 248-250. In 1946 the Federal Crop Insurance Corpora-
tion instituted a "continuous" contract which would be subject to
annual cancellation by either the farmer or the corporation. A
three-year contract was being used for wheat. See Agricultural
Finance Review, IX (1946), 71.
2This is the basis upon which the Federal Crop Insurance
Act was administered, i.e., rates were established on the basis of
yield experience. This resulted in some adverse selectivity from
year to year. For instance, local committees administering the act
in the Southern Great Plains advised against insuring in 1942 be-
cause seedbed conditions were good and premium rates and insured
yields were based on previous drought conditions. See Clendenin,
ibid, p. 254.
is known to exist. If premium rates are set to disregard the oc-
casional additional hazard the insurance carrier will be subsi-
dizing the insured during the times when such hazards are known to
exist. If premium rates are fixed at a level which will compensate
for such losses in the .long run, an incentive would be provided for
an adverse selectivity on a year-to-year basis. To prevent this
type of selectivity it appears that premium rates must be raised
when the additional hazard is known to exist.1 A farmer's yield
expectation, in comparison with his insured yield and premium rate
will determine whether or not he will use crop insurance.
Farmers Grow Two or More Crops
When farmers grow two or more crops but insure only one
crop, there will be a "substitution effect" in favor of the insured
crop in years when relatively poor yields appear probable and on
those farms on which the expected yield is close to the insured
yield.2 There will be a "scale effect" also, which tends to main-
tain the scale of enterprise in these instances. Under these con-
ditions the discounted value of the return from an insured acre is
greater than that from an uninsured acre and uninsured acreage will
be reduced relative to insured acreage. As yield prospects become
worse, the uninsured acreage may be eliminated.
As yield prospects increase above the levels for insured
yields the discounted value of the net return from an uninsured
acre becomes greater than that from an insured acre, and uninsured
1We wish to caution against overemphasizing the practical
importance of this particular problem. The occurrence of phenomena
which may indicate yields a year or more in advance may be rather
rare in spite of the incident related above.
This expectation is formed at or before the time of
seeding. It is based on knowledge of past yields of soil moisture,
of tilth conditions, of weed condition, etc., which the farmer
holds. The yield expectation may be influenced by judgment of some
other factors such as weather. In the analysis it is assumed that
prices remain constant.
crops may be substituted for insured crops, or insurance may be
2. All-Risk Crop Insurance and Resource Utilization
The effect of all-risk crop insurance on utilization of a
given land resource, on intensity of cultivation, on investment in
fertilizer, etc., may be determined by analysis of the relation-
ships of a farmer's insured yield to his yield expectation in a
given cost situation.
As long as yield expectations are well above the level of
insured yield input schedules will be set near the point of maximum
profit. Since the premium is a fixed cost per acre, the points of
maximum profit with respect to inputs will be the same as when in-
surance is not used.1 If yield expectations are close to or below
the insured yield, however, a pronounced change may take place in
the plans and operations of the firm. In this case the farmer may
restrict inputs to the level which is necessary to qualify for crop
insurance.2 Restricting inputs to this level eliminates any pos-
sibility of loss and in case crop conditions are very favorable a
net return may still be realized. The farmer therefore would cover
his costs if the yield is as expected and he would have a net re-
turn for management (1) if there is a complete crop failure or (2)
if crop conditions are very favorable. The farmer would prefer,
1With crop insurance the firm should operate closer to
these points than if insurance is not used because the limiting
effects of capital rationing and increasing risk would be reduced
or eliminated. Crop insurance may help to reach a position of
profit maximization, therefore.
2The condition attached to this analysis is that the farmer
must employ some minimum inputs in order to qualify for insurance.
In this case it is assumed that the cost of these inputs, plus
costs of harvesting a relatively poor crop, plus the insurance
premium, are equal to the insurance indemnity.
therefore, that the crop would be a complete failure or that con-
ditions would be unusually good. The worst possible situation is
to have yields with discounted value less than harvesting costs
under the insurance contract provision that such situation requires
the harvesting of the crop. If the discounted value of the insured
yield is at least equal to the farmer's investment in the crop the
farmer would avoid loss under any condition.2 In general the
closer the insured yield is to expected yield the greater the ten-
dency would be to reduce inputs to the level necessary to qualify
for the crop insurance indemnity. This explains in part why the
Congress, in an attempt to avoid losses inherent in over-insuring,
has found it expedient to reduce insured levels for the all-risk
O1ne farmer was found to be "planting flax" in North
Dakota in August. He was insuring the crop since the deadline for
planting had not been fixed. Crop failure was practically certain.
There are other examples of farmers continuing to plant and insure
when crop failure was almost certain. See Clendenin, "Federal Crop
Insurance in Operation," op. cit., p. 250.
2The 1947 amendment to the Federal Crop Insurance Act read
in part if 75 per centum of the average yield _on the in-
sured farm represents generally more protection than the invest-
ment in the crop in any area, taking into consideration recognized
farming practices, the Board shall reduce such maximum percentage
so as more nearly to reflect the investment in the crop in such
area ..." See 80th Congress, Ist Session, Public Law 320 (S.
1326), p. 1, Sec. 508(a). For a discussion of the reasons-for this
amendment see 80th Congress, 1st Session, Department of Agriculture
Aprprpriation Bill for 1948, Hearings before the Subcommittee of
the Committee on Appropriations, House of Representatives (April
19, 1947), pp. 1696-1700. Insurance may be written to cover an
average investment in the crop rather than a certain percentage of
average yield. This type of insurance has been used on an experi-
mental basis for corn and tobacco. See Report of the Manager of
the Federal Crop Insurance Corporation, 1947, op. cit., pp. 25,
30. This type of insurance has been sold on a more conservative
coverage than the yield type because prices constitute an addi-
tional hazard. In 1947 the F.C.I.C. was limiting coverage on to-
bacco to 75 percent of the average investment, or to about two-
thirds of the coverage which could be secured through the yield
type. By 1947 about 15 percent of the insured tobacco producers
had selected the investment type of insurance. In the case of corn
the coverage was equal to about one-half to two-thirds of the
coverage provided by yield insurance on basis of 75 percent of
average yield. See ibid., pp. 25, 30.
The general effects of all-risk crop insurance on resource
utilization by the firm may now be summarized. (1) When yield ex-
pectations are relatively poor, all-risk crop insurance will en-
courage a farmer to plant a crop on land which would not be seeded
if this insurance were not available. The inputs on this land will
be kept at the minimum required to qualify for crop insurance in-
demnities. Crop prospects could not become bad enough to dis-
courage seeding as long as. probable value of the insurance indem-
nity is equal to or greater than the cost of minimum qualifying
inputs. (2) When yield prospects are close to insured yields there
will be a general tendency to minimize inputs to the level required
to qualify for crop insurance indemnities. If yields actually turn
out to be better than expected the farmer will be worse off than
if he had made inputs to maximize net return at the given yield
expectations but if yields are worse than expected he will not lose
money. (3) Only when yield expectations indicate that the net re-
turn will be greater, consistently, than the difference between
insurance indemnities and the minimum qualifying inputs will inputs
be made at the level to maximize net return from the crop. It is
doubtful whether insurance would be used in this circumstance.
The question which was posed near the beginning of this
chapter, whether all-risk crop insurance could work successfully
according to standards developed previously, must be answered
largely in the negative. The reasons for this conclusion may be
summarized as follows:
1. If the yields on a farm trend either upward or down-
ward, those farmers having an upward trend in yields would find
that aggregate premiums would exceed aggregate indemnities over a
period of years and they would have a net loss through purchase
of this insurance, while those farmers having a downward trend in
yields would be subsidized through purchase of this insurance.
2. If premium rates are based on county averages, regard-
less of individual farm yield (as the F.C.I.C. has found expedient),
some farmers having a wide deviation in yields would benefit at the
expense of other farmers having a lesser deviation in yields. Only
a very peculiar relationship of yield deviations between high and
low yielding farms could equalize the probabilities of indemnities
among the farmers in a county. This relationship may not exist
except in rare instances.
3. If all the farmers do not purchase insurance, the far-
mers with relatively good yield expectations compared with their
insured yield would minimize the purchase of insurance and those
farmers with relatively poor yield expectations would tend to buy
insurance with greater frequency. This could result in adverse
selectivity among farmers in any season and a given group of far-
mers would tend to insure more heavily when yield prospects were
4. When farmers grow two or more crops with similar yield
variability but insure only one, they will expand the acreage of
the insured crop when their yield expectations are relatively low
compared with insured yields, and they will reduce this acreage
when yield expectations are relatively high.
5. When yield expectations are far enough above input
(costs) so that probable net return is greater than possible in-
surance indemnity less qualifying input (costs), the use of all-
risk insurance may encourage the maximization of net return. Under
these expectations, however, there would be little incentive to
carry insurance. When yield expectations are about equal to in-
sured yields, inputs may be minimized to the level which is neces-
sary to qualify for crop insurance. When yield expectations are
very poor, however, the continuation of minimum inputs to qualify
for crop insurance may be encouraged because the insurance indem-
nity will prevent loss. Use of this insurance may keep some land
in crop when crop prospects are poor; land that would not be
cropped if crop insurance is not available.
An issue which may be raised is whether, with a given farm
condition requiring indemnity, indemnity payments should be or
should not be varied in value directly, but not necessarily propor-
tionately, with the size of the crop harvested in the Nation. If
it is argued that.they should vary directly, the basis for argument
could be (1) that when short crops occurred each farmer would not
need to be fully reimbursed for "his" short crop because prices
would be higher than would occur otherwise,l and (2) that the cor-
relations between farmers' crop yields are high enough so that most
farmers would share in the higher prices. If it is argued that
they should be paid without consideration to the size of the crop,
the basis for argument could,.be (1) that the crop yield experienced
by any particular farmer bears no consistent relationship to the
national yield,2 and (2) that even if yields are positively corre-
lated over wide areas, price and storage programs may, in the
'The elasticity of demand for many of the major farm crops
in the United States has been found to be between zero and minus
unity so that, ceteris paribus, a small crop sells for more than
a large crop. See Henry Schultz, The Theory and Measurement of
Demand (Chicago: The University of Chicago Press, 1938), esp.
pp. 229-230, 275, 331-332, 400-401, 427, 481-482, and 499.
2A similar premise has been used elsewhere in consideration
of one of the problems involved in forward pricing. See D. Gale
Johnson, Forward Prices for Agriculture, op. cit., Chapter XIII
and D. Gale Johnson, "A Price Policy for Agriculture, Consistent
with Economic Progress, that will Promote Adequate and more Stable
Income from Farming," Journal of Farm Economics, XXVII (1945),
future, help to reduce the more violent of the price fluctuations
which have been due to yield variations.l
When stated as above, the argument is rooted in empirical
data and, therefore, the answer derived will be of limited, al-
though perhaps valuable, application. Using an a priori argument,
however, if the crop yield on any individual farm bears no par-
ticular or consistent relationship to the,national yield then there
is little or no argument for indemnity payments which vary directly
with the size of the crop even if the elasticity of demand for the
crop is between zero and minus unity2 and even though there may be
significant correlations between crop yields in different areas of
Other arguments for not varying indemnity payments directly
with the size of the crop harvested in the Nation are, that under
such a provision (1) the actuarial basis for calculating probable
indemnities on a farm or in an area would not be known at the time
insurance is sold, and (2) the farmer buying insurance would not
know the value of his indemnity in the event yields are below in-
sured yields. We conclude, therefore, that our analysis may be
based on the assumption that indemnity payments should not be
1For discussion see Geoffrey S. Shepherd, op. cit., Chap-
ters XIV-XVIII and D. Gale Johnson, Forward Prices for Agriculture,
op. cit., Chapters X and XII.
2Cf. Henry Schultz, loc. cit. The fact that this type of
elasticity exists does not guarantee that a small crop of wheat,
for instance, will sell at a higher price than a large crop because
(1) as previously indicated (above, pp. 2, 37-38) total agricul-
tural output in the United States may be relatively stable, and
(2) fluctuations in demand may have impacts of greater magnitude
on price than do fluctuations in supply.
Correlations between crop yields in different areas or
between the national yield of different crops may be insignificant.
See for example Geoffrey S. Shepherd, The Proper Size and Location
of Corn Stabilization Stocks, Iowa Agricultural Experiment Sta-
tion, Research Bulletin 321 (Ames, Iowa, 1943), pp. 9 and 10, and
D. Gale Johnson, Forward Prices for Agriculture, op. cit., pp.
varied directly with the size of the crop grown in the Nation.
The indemnity should be paid (1) in terms of the commodity insured
or (2) in terms of some fixed price or forward price for the
A basic assumption underlying the theory of area-yield in-
surance is that the arithmetic mean of the yields received in any
one year in an area will reflect the physical crop conditions faced
by any farmer in the area. If this assumption is correct,then any
farmer may protect himself against the occurrence of adverse crop
conditions by buying area-yield insurance. The insurer would be
insuring the physical crop conditions faced by the farmer rather
than his yield. Whenever the mean area-yield falls below the area
yield insured by the farmer then he would be eligible to receive
an indemnity which would vary directly with the difference between
the mean area yield for the year and the insured yield. The pre-
mium paid by the farmer would be based on the actuarial probability
of mean area yield falling below the insured yield.
We shall attempt to determine whether area-yield insurance
can provide farmers with adequate protection against low yields
which are due to adverse crop conditions and whether area-yield
insurance can work successfully according to the standard pre-
1. General Concepts
Six general concepts are involved in area-yield insurance.
These are (1) the area, (2) nbrmal yield for the area, (3) the in-
sured yield for the area, (4) the area yield in any one year, (5)
the premium, and (6) the individual farmer's acreage which is to
The area may be part of a township, a township, part of a
county, a county, several counties, or a type-of-farming area.1
It should be so small that, in general, weather would be uniform
throughout and it should be so delineated that the weather expe-
rienced in a season would have a similar effect on yields through-
out the area. If these conditions were fulfilled any farmer in
the area would find that indemnities were received in years when
adverse crop conditions were experienced.
'A type-of-farming area may be defined as an area in which
one system of farming is dominant, or as an area in which two or
more systems are interwoven into a pattern. The area may be de-
lineated so that within any one boundary the same pattern of change
may exist. The boundaries of a type-of-farming area may change as
ecological factors change. Cf. John D. Black, Marion Clawson,
Charles R. Sayre, and Walter W. Wilcox, Farm Management (New York:
The Macmillan Company, 1947), pp. 384-386; C. A. Bonnen and B. H.
Thibodeaux, A Description of the Agriculture and Type of Farming
Areas in Texas, Texas Agricultural Experiment Station Bulletin 544
(College Station, 1937), pp. 68-91; H. C. M. Case and K. H. Myers,
Types of Farming in Illinois: An Analysis of Differences by Areas,
Illinois Agricultural Experiment Station Bulletin 403 (Urbana,
1934); Marion Clawson, Walter U. Fuhriman, George T. Blanch, Types
of Farming in Utah, Utah Agricultural Experiment Station Bulletin
275 (Logan, 1936); I. G. Davis, Types of Farming and Type of
Farming Areas in Connecticut, Storrs Agricultural Experiment Sta-
tion Bulletin 213 (Storrs, 1936); F. F. Elliott and R. H. Rogers,
Types of Farming in South Dakota, South Dakota Agricultural Ex-; 't.
periment Station Bulletin 238 (Brookings, 1929); F. F. Elliott,
Fesse W. Tapp, and Rex E. Willard, Types of Farming in North
Dakota, U.S.D.A., Technical Bulletin 102 (Washington, 1928); E. B.
Hill, F. P. Riddell, and F. F. Elliott, Types of Farming in Michi-
gan, Michigan Agricultural Experiment Station, Special Bulletin
206 (East Lansing, 1930); J. A. Hodges, F. F. Elliott, and W. E.
Grimes, Types of Farming in Kansas, Kansas Agricultural Experiment
Station Bulletin 251 (Manhattan, 1930); C. L. Holmes, Types of
Farming in Iowa, Iowa State College Agricultural Experiment Station
Bulletin 256 (Ames, 1929); Neil W. Johnson and M. H. Saunderson,
Types of Farming in Montana, Montana Agricultural Experiment Sta-
tion Bulletin 328 (Bozeman, 1936); Neil W. Johnson and Rex E.
Willard, Nature and Distribution of Types of Farming in Washington,
Washington Agricultural Experiment Station Bulletin 301 (Pullman,
1934); Bruce Poundstone and Walter J. Roth, Types of Farming in
Kentucky, Kentucky Agricultural Experiment Station Bulletin 357
(Lexington, 1935); W. J. Spillman and F. F. Elliott, "Type of
Farming Studies," (Washington: U.S.D.A., Bureau of Agricultural
Economics, January 1928, mimeographed); E. C. Young and F. F.
Elliott, Types of Farming in Indiana, Purdue University Agricul-
tural Experiment Station Bulletin 342 (Lafayette, 1930).
Type-of-farming areas should be divided in some cases where
yield conditions are not homogeneous throughout the areA. It is
essential that the area on which yields are based be so small that
the yields in any year will not reflect the crop conditions faced by
any farmer in the area. The size and shape of the area would be
determined by ecological, geographic, and economic factors. In
the Red River Valley of North Dakota three of four townships might
be included in the area. In the Lower Yellowstone Valley of
Montana, where some of the land is irrigated and some is not, one
area including the irrigated land might be (say) 20 or 30 miles in
length with adjacent non-irrigated land being in another area.
Where specialty crops, truck crops, fruit, etc., were grown the
area might be divided according to major crop grown. In some cases
the equivalent of several counties might be included in one area
while in other cases a portion of a township might constitute an
The Normal Yield
The normal yield might be defined as a 10 or 15 year moving
average of yields adjusted for trend. The normal yield would be
iSee especially Davis, op. cit., Neil W. Johnson, Farm Ad-
justments in Montana. Study of Area VII: Its Past, Present and
Future, Montana Agricultural Experiment Station Bulletin 367
(Bozeman, 1939), pp. 14-29; and Neil W. Johnson, "Considering Farm
Adjustments in Subarea 33, Type of Farming Area VII, Montana,"
(Washington, U.S.D.A., Bureau of Agricultural Economics, 1939,
2The main ecological factors to be considered are water re-
lationships, temperature relationships, light relationships, and
the form and availability of crop nutrients. These determine the
physiological limits of crop production. Some geographic and eco-
nomic factors to be considered are market demand, technological
production conditions, transportation costs, and patterns of change
in crop production. These latter factors help to determine the
type-of-farming area and to explain the reason for the type de-
veloped. All of the above factors have been discussed under the
title of "ecological crop geography." See K. N. W. Images, Eco-
logical Crop Geography (New York: The Macmillan Company, 1942),
Chapters I and IX.
the mean area yield that would be realized if crop conditions were
"normal."l A moving average adjusted for trend might be "practi-
cal" for use in area-yield insurance because the average could be
based on an adequate sample of farms.2
The Current Yield
The current yield in any one year could be computed for
the area in a preliminary manner by methods currently in use by
the Agricultural Statistical Service, B.A.E., with final estimates
and area averages being made after harvest. Farmers who were in
areas where it was clear that an indemnity would be paid could
apply for partial payment at time of harvest. The final yield es-
timate for the year might be made later and final adjustment made
on basis of this computation.
The Insured Yield
When a farmer bought area-yield insurance he would be in-
suring that current area yields would be equal to normal area yield
or to some percentage of normal yields. If a farmer chose to in-
sure normal yield he would be eligible for an indemnity any time
IThis might assume that expected yields will be distributed
in a symmetrical manner about the normal yield. As a matter of
fact, there may be a tendency, in local areas, for yields to be
very low in a few years and moderately high in many years. The
distribution in such cases would be skewed to the left. See G. S.
Shepherd, Agricultural Price Policy, op. cit., pp. 344-346. The
opposite skewness appears to be typical for the nation, however,
i.e., the frequency distribution of some yields is skewed to the
right. For example, the following measures of central tendency
describe wheat yields for the United States for 1920-1945: mean
= 14.5 bushels per acre; mode = 13.2 bushels per acre; and median
= 14.0 bushels per acre. See Agricultural Statistics 1946.
op. cit., p. 7.
2The same method could not be applied as well in the case
of the all-risk crop insurance because (1) the statistical work
involved in calculating a moving average for each farm and in ad-
justing this average for trend would be costly and time consuming
and (2) the reliability of an average so constructed and adjusted
might be in doubt. Changing farming practices, a new manager, for
instance, might make all previous calculations inapplicable.
the current area yield fell below the normal yield. If he chose
to insure for, say, 75 percent of the normal yield he would receive,
an indemnity whenever the current yield was less than 75 percent
of the normal yield. His indemnity would vary directly with the
difference between his insured yield and the current area yield,
when the latter was smaller.
The premium to be paid would be based on historical yields
in the area adjusted for trend and would be calculated according
to actuarial probabilities of indemnity. The percentage of normal
yield to be insured could be stated by the farmer and the premium
would vary directly, but not necessarily proportionately, with the
yield for which he elected to insure. For instance, if a farmer
elected to insure for the full normal yield his premium might
average five bushels per acre, for example, but if he elected to
insure for 75 percent of normal, his premium might be two bushels
Premiums could be calculated on the basis of equal annual
payments by the insured or the premium could be collected only in
years when mean area yield exceeded normal yield. In the latter
case premiums could be the difference by which current mean area
yield exceeded normal yield. The choice between these two methods
could be made by the farmer buying the insurance contract.
The individual farm acreage to be insured would be deter-
mined at the time that contracts were drawn. The contract would
be binding upon each party. Such a provision could be enforced
in this type of insurance because the insured could be allowed some
discretion in the acreage to be seeded in a given year. If weather
adverse for seeding should develop in the spring, for instance, so
that a farmer decided against seeding some of his acreage, his
action would be a matter of indifference to the insurance carrier
because, if an indemnity was to be paid to the farmer, his own
action would have little or no influence on the amount of the
To prevent an adverse selectivity from developing through
time, however, it probably would be necessary for the insurance
carrier to add the provision that a certain acreage, about 40 per-
cent of the insured acreage for example, would have to be seeded
on any farm in order to make that farm eligible for an insurance
indemnity in that year. If such a provision is not included it is
conceivable that in an area where the insured crop is "marginal"
poor price prospects and unfavorable seeding conditions might pre-
clude the seeding of a sufficient acreage in a given year to es-
tablish an adequate basis for calculating the annual area yield.
To make certain that a farmer does not insure considerably
in excess of the acreage he intends to seed, thus covering more
than his normal insurable interest and turning-the insurance into
a gambling device, it may be necessary to place some upper limits
on the acreage that can be insured by any one farmer. (1) The
upper limit for insurable acreage might be based on past acreage,
much after the method used by the A.A.A. in determining base allot-
ments for the production control program used in the United States
in the 1930's. (2) To take account of the dynamics of the farm,
however, a farmer might be allowed to insure on the basis of a
moving average of his seeded acreage for some five years. (3) The
insurance carrier might set an upper limit for the total acreage
to be insured within the area and allocate this acreage to farmers
(a) on the basis of arable land in the farm, (b) on basis of
acreage of crop seeded in past years, or (c) on basis of relative
production, yield times acreage, of the individual farms. For
reasons given below the latter method may be most equitable but
actual trial and experience may be necessary in order to decide
which method is most desirable.
2. General Theory and Assumptions
Technical and Technological Conditions Change
If normal area yields and premiums are adjusted for trend,
as yield expectations for the area change, so that a "correct"
actuarial relationship will exist at any time between premiums and
insured area yield, then the insurance carrier may be indifferent
about whether the trend of yields in the area is upward or down-
ward. The insurance carrier may be indifferent also about the
yield trend on any individual farm because all farmers in the area
will participate in a similar premium and indemnity scale.
Mean Yields for Farms in the Area Differ
Mean yields of individual farms in an area may differ
widely (see Table 4). This fact does not change the actuarial
problem of the insurance carrier because premiums and indemnities
are based on area averages rather than on individual farm data.
Whether the farmers with different mean yields will all be pro-
tected against adverse crop conditions depends (1) on the degree
of correlation between area yields and the crop conditions faced
by the individual farmer, and (2) on the relative variation in
yields among the individual farms in the area. Assuming that the
degree of correlation is high ahd significantly farmers may be pro-
tected against yield variations by insuring their seeded acreage
providing that the variations among farms are similar in bushels
iThis assumption is a matter for empirical verification.
Examples of yield experiences among selected farms are given below.
When the correlation is found to be high it may be assumed that the
relationship between area yields and crop conditions faced by the
farmers is close. A low correlation between area and farm yields
does not prove that this relationship does not exist, however, be-
cause a lack of correlation might be due to the farmer's own
or pounds per acre. It may be assumed, however, that farmers with
relatively low yields in an area will have a lower yield variation,
in bushels or pounds per acre, than the farmers with relatively
high yields. If this is the case the farmers with higher yields
would have to insure for more than their seeded acreage in order
to obtain complete protection against yield fluctuations.
The solution for the "ideal" acreage to insure may be
obtained as follows:
1. Assume first that the percentage variation in yields
is the same for all farms in an area. Then to be "fully" insured
a farmer would insure an acreage which is equal to planted acreage
times mean yield of the farm divided by mean yield of the area.
For example, if a farm had an average of 15 bushels of wheat per
acre and the area had an average of 10 bushels per acre and if
seeded acreage is 400 acres, insured acreage would be 600 acres.
2. Assume next that the percentage variation in yields is
not the same for all farms in an area. Then to be "fully" insured
a farmer, in addition to the adjustment made under the first as-
sumption, would vary insured acreage according to seeded acreage
times the coefficient of variation of farm yield divided by the
coefficient of variation of the area yield. For example, suppose
that the C.V. of the yield of the farm in the above example is .9
and that of the area is .8 then insured acreage would be 600
(.9 + .8) or 675 acres.
The acreage to insure to maximize stability would be equal
Sx ean vield of farm. C.V. of farm yield
to: (seeded acreage) x (mean yield of area) x (C,. of .aea.yiei)J*
Using the above figures as an example in the formula the
acreage to insure would be as follows: 400 (1) x = 675.
No particular formula, however, will determine whether the
acreage insured by a farmer will provide him with the equivalent
of complete yield stability. The actual result will depend on the
empirical yield situation in the area. Making the assumption that
the percentage variation in production is more uniform among farms
in the area than is the variation in terms of bushels or pounds
per acre then the most equitable limit to put on the farmer's in-
surable acreage would be determined by setting an upper limit on
the total acreage to be insured in an area and by allocating this
acreage base to farmers on the basis of relative production, yield
times acreage, of the individual farms in the area. Such a method
would allow the farmers in an area to be covered by insurance to
the extent of relative output and it would prevent the insurance
carrier from offering insurance on a farm in excess of the farmer's
normal insurable interest. In areas where mean yields of indivi-
dual farms do not differ to any marked degree, justice could be ob-
tained by setting the limit on insurable acreage within some 105
percent or 110 percent of average seeded acreage on the farm.
All Farmers Do Not Buy Insurance
The insurance carrier may be indifferent about which far-
mers buy insurance within an area, because all premiums and indem-
nities are based on area yields. As discussed previously, however,
farmers may be able to estimate area yields a year or two in ad-
vance with greater accuracy than would be inherent in the formula
used by the insurance carrier. The base we have suggested for use
in area-yield insurance, the moving average adjusted for trend,
implies that the elasticity of expectations for yields is near
unity.1 Actually it may be greater or less than unity and farmers
1Hicks used the term 'elasticity of expectations' as "the
ratio of the proportional rise in expected prices of a commodity
to the proportional rise in its current price." See J. R. Hicks,
Value and Capital (Oxford University Press, 1939), p. 205. We use
the term in a similar sense, meaning that if a rise, or fall, in
yields is expected to continue at the same rate the elasticity of
expectations is unity. For an appraisal of how farmers actually
do form their expectations in regard to yields see T. W. Schultz
and 0. H. Brownlee, "Two Trials to Determine Expectation Models
Annlionhp ton Aoritenil-tre." lo.- cit.
may be well aware of that fact. Consequently they might buy in-
surance heavily when yields are expected to be lower than the for-
mula indicates and they might drop out of the program when they
expect yields to go above those indicated by the formula. If their
expectations are correct and the terms of the contract allow them
to act in this way it is possible!that a year-to-year adverse
selectivity might result.
Various devices might be used to overcome the possibilities
of such an adverse selectivity. (1) An initial entry fee and/or
a re-entry fee might be charged. These fees could be adjusted to
prevent intermittent participation. Under certain circumstances
they might be refundable. (2) A long-term contract, a three, four,
or five-year contract for instance, with early deadlines for appli-
cation and cancellation, might be the only kind offered. (3) The
insurance carrier might increase premiums, or lower normal yields,
when lower area yields are expected, provided the formula does not
reflect the change in expectation. The opposite might be done when
higher yields than indicated by the formula are expected.
The third device might be considered more desirable in an
actuarial sense but it would involve more administrative detail
than the first and second. If the premium rate used reflects cur-
rent yield expectations, the use of area-yield insurance may con-
tribute toward an optimum allocation of resources.1 The compromise
among the above methods probably should depend on the circumstances.
In a semi-arid region in a period of severe drought, for instance,
an optimum use of resources, from standpoint of soil conservation,
may be encouraged by giving some weight to the third device. In
iWe define an optimum use of resources as a condition
existing when any small change in the production pattern leads to
a combination of decrements and increments in output such that
there is no system of exchanges whereby the increments will be
accepted voluntarily as compensation for the decrements.
another area where yields may be more stable, or less predictable,
the third device might be disregarded.
3. Effects of Area-Yield Insurance
on Resource Utilization
The effect of area-yield insurance on the utilization of a
given land resource, on intensity of cultivation, on investment in
fertilizer, etc., may be determined by analysis of the effect of
this insurance on profit expectations. Since the occurrence of
indemnity is not influenced by the farming practices adopted by a
farmer, his marginal costs and marginal returns will not be altered
by the use of insurance. The farmer will make inputs on the scale
determined by his own yield expectations.
Yield insurance on an area basis will not distort resource
utilization, therefore, as was probable in the case of all-risk
crop insurance. Capital rationing and increasing risk, which
otherwise might be effective at higher levels of output, will be
reduced and this will encourage a use of resources which is consis-
tent with the type of marginal analysis that ignores capital
rationing and increasing risk.
4. Illustrations and Criticism
A basic assumption of the theory of area-yield insurance
is that annual mean area-yield in any year will reflect the physi-
cal crop condition faced by a farmer in the area. The validity
of this assumption will depend, to a considerable degree, on the
boundaries established for the area and on the homogeniety of the
area in production of the crop insured. The practical value of
area-yield insurance in providing the equivalent in yield stability
for an individual farmer will depend, therefore,-on the empirical
situation in any locality, i.e., on how closely the annual farm
yield and the annual mean area yield will be correlated from year
to year. The closer this correlation is, the more effective will
be area-yield insurance in providing the equivalent of yield
stability for a farmer in the area.
Illustrations of how an area-yield insurance program might
function can be made by applying the basic plan to a series of farm
yields as is done in Table 6. The unadjusted annual yield data
can be averaged to determine (1) the mean annual yield for the
area, and (2) the mean yield for each farm in the area (Table 6,
Part A). The area yield for a base period can be used as the in-
sured area yield. Individual farm yields would be adjusted upward
when the annual area yield is below the insured yield and downward
when the annual area yield is above the insured yield (Table 6,
Part B). A comparison of the yearly deviation from the mean farm
yield can be made to determine the extent of yield stability
achieved by the use of area-yield insurance. In the models pre-
sented in Table 6, for example, the average deviation of yields of
farm number 1 is 4.7 bushels per acre without insurance and 1.9
bushels per acre with insurance.
Since the average deviation, and the ranges between high
and low yields, are about one-third as great with insurance as
without it, we may conclude that area yield insurance would sig-
nificantly increase yield stability under the conditions illus-
trated. Since no effort was made, in this illustration, to group
farms by type of farming area, by size, or by similarity in yield
trends, etc., we conclude that this represents less than the op-
timum conditions that could be established for an area-yield in-
surance program. Further refinements of areas should increase the
effectiveness of area-yield insurance in reducing yield uncertainty.
The illustrations presented in Table 6 are based on the
plan of insuring on the basis of full area yield, in which case
premiums would be paid in years when area yield is above the mean.
ILLUSTRATION OF EFFECTS OF AREA-YIELD INSURANCE ON WHEAT
YIELDS OF FARMS IN PRATT COUNTY, KANSAS, ASSUMING
ALL FARMERS INSURE FOR MEAN AREA YIELD
Farm Number .
Year 1 2 2 4 Area
A. Annual Yields
1946 12.0 18.8 22.1 14.9 16.9
1945 15.0 18.9 15.7 12.8 15.6
1944 18.2 21.2 24.0 20.8 21.0
1943 13.8 15.9 11.0 9.7 12.6
1942 20.0 24.0 18.0 22.3 21.1
1941 27..8 22.4 22.0 19.6 23.0
1940 7.0 6.0 4.4 9.4 6.7
1939 20.6 22.2 21.7 17.0 20.4
1938 12.8 12.0 15.1 9.6 12.4
Mean Yield 16.4 17.9 17.1 15.1 16.5
Deviation 4.7 '4.4 '4.9 4.3 4.6
B. Equivalent Annual Yields Using Area-Yield Insurance.
1946 11.7 18.5 21.8 114.6 16.6
1945 16.0 19.9 1 16.7 13.8 16.6
1944 13.8 16.8 19.6 16.4 16.6
1943 17.8 19.9 15.0 13.7 16.6
1942 14.5 19.5 13.5 17.8 16.6
1941 21.4 16.0 15.4 13.1 16.6
1940 16.9 15.9 14.3 18.3 16.6
1939 16.8 18.4 17.9 13.2 16.6
1938 17.0 16.2 17.3 13.8 16.6
Mean Yield 16.4 17.9 17.1 15.1 16.6
Deviation 1.9 1.5 2.1 1.7 1.8
..._____....... ,..______ _....
Source: Data on yields were gathered by
a,-,i-n1,n1r .rnnnnminr Kanan Snta-p CnllPorp_
In the yield situation illustrated in Table 6, Part A, we may use
a method in which indemnities are paid only when insured area
yield is some fraction of the mean area yield. If these farmers
had insured for 85 percent of the mean yield and had paid premiums
in only the years when area yield was 110 percent of average, the
mean of the average deviation of yields would have been 2.1 bushels
per acre, as compared with 4.6 bushels per acre when insurance was
not used. The advantage of this method is that the magnitude and
frequency of premium and indemnity payments may be reduced.
Data for five farms in Montana and for five in North Dakota
are presented in Tables 7 and 8.
WHEAT YIELDS PER SEEDED ACRE ON FIVE FARMS
IN ALTON COMMUNITY, FERGUS COUNTY, MONTANA
Year Area A Area B
1930 17.8 17.8 10.0 10.0
1931 12.0 12.0 6.7 7.1
1932 .5.3 8.3 .0 .0
1933 13.8 14.0 10.0 16.5
1934 9..7 9.8 13.1 15.8
1935 12.8 12.9 12.7 17.1
1936 9.5 9.3 10.0 9.5 9.1
1937 12.5 5.5 6.0 17.0 12.8
1938 27.5 20.5 22.5 23.5 27.5
1939 13.4 14.3 14.3 13.4 14.2
1940 13.4 13.5 13.0 14.1 22.4
1941 15.8 13.0 13.2 11.9 16.1
1942 16.9 14.0 13.0 13.7 16.7
1943 18.8 15.7 14.0 14.7 18.0
1944 14.1 15.5 15.3 14.2 19.5
1945 16.0 16.2 15.5 15.8 26.3
1946 9.0a 8.1a 6.4a 12.2 15.1
Average Yield 14.8b 12.8 13.8 12.5 15.5
A.D. Without Ins. 3.4 3.1 2.9 3.2 4.8
A.D. With Ins.c 1.6 1.0 .7 1.3 1.3
bDeflated to 1930-1946 base.
CAll farmers insure on basis of area yield.
Source: Data obtained from records in Fergus County P.M.A.
office at Lewistown, Montana.
WHEAT YIELDS PER SEEDED ACRE ON FIVE NORTH DAKOTA FARMS
Counties, Area A Counties, Area B
Year Dickey Dickey Mountrail Divide Williams
1923 5 6 10 17 21
1924 15 10 11 21 20
1925 16 14 25 20 23
1926 4 7 9 18 17
1927 10 13 10 17 25
1928 16 12 24 24 0
1929 13 12 12 17 15
1930 15 14 4 15 8
1931 7 9 0 0 0
1932 13 13 18 16 7
1933 11 2 13 14 0
1934 3 0 0 1 0
1935 12 8 4 7 5
1936 1 0 1 0 0
1937 8 5 0 0 0
1938 0 3 9 11 11
1939 12 10 9 12 12
1940 8 5 8 19 14
1941 18 16 22 44 32
1942 13 20 20 34 20
1943 7 12 21 38 24
1944 20 15 19 28 26
Average Yield 10.3 9.4 11.3 17.0 12.7
A.D. Without Ins. 4.6 4.4 6.6 8.5 8.1
A.D. With Ins. 1.6 1.4 2.5 1.1 2.6
_ _,_ _ I ,_ __,_ _
Source: Unpublished material
St. Paul, Minnesota.
of Farm Credit Administration,
The basic assumption underlying the theory of area-yield
insurance, that the area mean yield in a year would reflect the
physical crop conditions faced by any farmer, has been found con-
sistent with the cases thus far examined.1 A criticism may still
be made, however, that in some cases the indemnities may be paid
to a farmer in a year when his yields are better than average
10ther cases involving more than 100 farms have been studied
with substantially similar results. The farms in Table 7 are from
a small community and could be handled as one area with about the
same reductions being made in yield variability through use of in-
surance. They were divided for illustrative purposes on the basis
of yield similarities. The two areas in Table 8 are from opposite
corners of the State. Many more farms would be included in an area
in actual practice. The data presented indicate some of the varia-
tions that may be tolerated in delineating areas.
and may not be paid sometimes when his yields are below his.aver-
age. This condition should be the exception rather than the rule.
Granting, however, that the exception may occur we shall examine
the content of the criticism.
It was stated, in Chapter III, that a function of specific
risk insurance was to provide insurance against the occurrence of
some specific event which is deemed adverse to the insured. This
is the nature of all accident and disaster insurance. The condi-
tions which the insured may face are insured rather than the out-
come of his operation. We may argue, just as logically perhaps,
that the object of crop insurance should be to insure the minimum
conditions under which the farmer is to operate rather than the
outcome of his operation. In fact, to guarantee the latter is to
insure the farmer's own action which is the thing that makes the
all-risk crop insurance unworkable, as we concluded in Chapter IV.
It is necessary to separate the causes of fluctuations in yields
in order to insure those caused by variations in physical crop con-
ditions and to avoid insuring those caused by variations or mis-
takes in management. The above criticism lacks content, therefore,
when it is applied to the actuarial features of area-yield in-
surance, or when it is .used to imply that area-yield insurance may
have an undesirable effect on resource utilization. We should
grant, however, that in cases where the relationship between in-
demnities and low yields is inconsistent some undesirable income
effects may result.
5. Some Special Problems of Area-Yield Insurance
A plan for area-yield insurance might be criticized because
the policy might provide adequate protection against localized
damage occurring in part of an area such as might be caused by hail
storms, local floods, or localized insect infestations. Crops in
a small part of an area may be completely destroyed and the average
yield in the area may be reduced (say) only 10 or 15 percent below
normal yield. For the farmer who has purchased insurance and who
loses his crop, through flood or hail, for instance, it would be
small consolation to receive an indemnity which covers only 10 or
15 percent of his loss.
Insurance against damage from local hail storms might be
obtained by attaching a hail riders to the regular insurance con-
tract in which case losses might be settled by inspection -- a
practice which has been in force in many areas for some time. At
least two unique difficulties may be anticipated: (1) Farmers in
a hailed-out section might be placed in position to collect a dou-
ble indemnity. (2) If the yields in the hailed-out section are
used in computing the area average, the farmers in the non-hailed
section of the area might collect an indemnity which is not
The solution might be reached as follows: (1) The section
in which hail occurred would be declared a "hail section." (2) If
yields in the rest of the area are normal, or above the farmer's
insured yield, the farmers in the hailed section would collect an
indemnity based on percent damaged by hail and no other indemnity
would be forthcoming. Farmers in the rest of the area would receive
1The rider would apply only in case damage was not uniform
over the area. The cost of this rider would be only a fraction,
therefore, of present hail insurance premiums and rates might be
uniform over a wide area, such as a state. Some people are of the
opinion that hail damage tends to be uniform over wide areas. For
instance E. K. Bowman, Chairman of the State Board of Hail Insur-
ance for Montana, has stated, "I am still very reluctant to con-
clude that certain parts of Montana are real hail belts .. A
careful examination and comparison of the maps convinces me that
the extent of any hail belts is doubtful .. This applies
to the parts of Montana east of the mountains .". See E. K.
Bowman, "Are There Hail Belts in Montana?", Montana Farmer-Stock-
man (June 1, 1947), p. 39.
no indemnity. (3) If, prior to the hail storm, indicated yields
were below normal in the area (or if yields in the non-hailed sec-
tion were previously found to be below normal) settlement might
be determined as follows: (a) Farmers in the non-hailed section
would be indemnified on the basis of their area yield insurance,
according to yields received in their section. (b) Farmers in the
hailed section would receive a similar indemnity plus an indemnity
based on the percentage of damage done to their growing crop.1
Certain parts of a township or county are likely to be more
susceptible to flooding or to "drowning out" than are other parts
or sections. Also some crops are hurt by standing water more
easily than are other crops. A crop may be hurt more easily by a
heavy rain at one stage of development than at another stage. Some
fields may be flooded because the farmer did not provide ditches,
or because the land was summer followed, or because the land lacked
natural drainage facilities. Most of the flooding which occurs in
one section of an area but not in another is, therefore, either
(1) caused by action, or inaction&, of the farmer, or (2) due to
special topographic features and soil characteristics.
Where all parts of an area are equally susceptible to
flooding no special problem arises because, in case of flooding or
drowning out, area yields would be influenced by the flooding and
farmers would be indemnified accordingly. The general solution to
the problem of flooding, therefore, is to delineate the areas so
that any land which can be considered as peculiarly subject to
iThe total indemnity may be calculated as follows:
Let I = total indemnity,
Yi = insured yield,
Ia = indemnity due from area-yield insurance, and
h = percent hail damage.
Then Yi Ia = balance of crop left after area-yield
indemnity is calculated and I = Ia + h (Yi Ia).
flooding is segregated in an area separate from other land. Normal
yields and current area yields would be derived from the same base.
There may be no other way to write area-yield insurance to protect
a farmer against flooding. If there is a section within an area
susceptible to flooding, a special premium and indemnity scale
would be required in order to protect the farmers in that section
against flooding. Since average yields throughout the area would
be affected by yields in the section which was flooded, the farmers
in the non-flooded area might be indemnified in years when they had
good crops. This would not be a desirable practice. Land which
is peculiarly susceptible to flooding, therefore, should be placed
in a separate area.
Localized Insect Infestations
Where an insect infestation is general over an area no
special problem exists and the usual provisions of the insurance
contract would provide a compensating indemnity. When the infesta-
tion is localized in one section of an area, however, a peculiar
problem would exist. Where the infestation occurs indemnities
would be inadequate. Where it does not occur indemnities might
exceed the damage done. This problem is peculiar because areas of
insect damage are seldom as clear cut as are areas of hail damage,2
for instance, and insect damage does not persistently reoccur in
some local section as do floods. In view of the fact that it may
not be practical to redraw area boundaries according to the
IThe relative economic importance of local insect infesta-
tions compared with non-localized infestations covering an area is
difficult to generalize. It seems evident, however, that the more
damaging infestations are not localized. See for instance, H. B.
Mills, 0. B. Hitchcock, and Ralph Schmiedeskamp, Montana Insect
Pests 1945 and 1946, Montana Agricultural Experiment Station Bulle-
tin 442 (1947), pp. 4-18.
2If insect infested areas could be defined as clearly as
areas of hail damage, the plan we suggested for dealing with local
hail storms could be applied to insect infestations.
potentialities of an insect infestation, we may conclude that no
special provision will be made to compensate for the possibility
of an insect infestation localized in a small section of an area.
Changing Cost-Price Relationships
Another problem is that changing cost-price relationships
may influence yield expectations to such a degree that actuarial
data in use would be incorrect. This criticism may have merit in
direct proportion to the ability of farmers to alter output in re-
sponse to changing market prospects providing that the insurance
carrier is prevented from changing premium and indemnity rates to
correspond with the changing market prospects. The criticism,
however, is limited by two considerations: (1) Farmers are re-
stricted in the speed and extent to which they will alter produc-
tion plans to meet changing market conditions because of (a) their
uncertainty about prices and output, (b) financial insecurity and
capital rationing, (c) increasing risk, and (d) fixed costs in crop
production. The fact that farmers are unable to make accurate
price forecasts may account for a large part of this rigidity.1
When higher product prices are anticipated farmers attempt to farm
their land more intensively to increase yields over what yields had
been when product prices were relatively low.2 Higher prices may
induce higher yields and lower prices may induce lower yields.3
1Cf. D. Gale Johnson, Forward Prices for Agriculture,
op. cit., Chapter VII, Johnson, "Contribution of Price Policy to
the Income and Resource Problems in Agriculture," loc. cit.
2Consider the trend of yields during World War II. See
Sherman E. Johnson, loc. cit. The discussion is based on the
assumption that changes in farm costs lag behind changes in farm
3This can be demonstrated with the aid of conventional
marginal analysis diagrams. We would argue, however, that farmers,
especially those on family type farms, are severely restricted in
the degree to which they can adapt resources to a changing cost-
price situation. Cf. John M. Brewster and Howard L. Parsons, "Can
Prices Allocate Resources in American Agriculture?", Journal of
Farm Economics, XXVIII (1946), 938-960, and D. Gale Johnson, For-
ward Prices for Agriculture, op. cit., Chapters V and VII.
(2) The insurance carrier may have more complete information about
prices and markets than does the individual farmer and the carrier
may be able to predict prices with greater accuracy. The essence
of the carrier's problem is to determine the incidence of these
market changes and market prospects on the normal area yield. If
the insurance carrier is allowed some administrative discretion
in changing normal area yield to meet the new cost-price relation-
ship, the carrier should be able to state a normal area yield as
accurately as can the farmer who is faced with the decision of
While the effect of market changes on yields may be con-
siderable, the importance of the above problem to the success of
area-yield insurance should not be exaggerated. In actual opera-
tion, the insurance carrier may quickly detect the presence of an
adverse selectivity among areas by comparing premiums and indem-
nities between areas with the relative percentage of farmers pur-
chasing insurance in different areas. Furthermore- it generally
requires two or three seasons for market changes to have much ef-
fect on yields. In cases where markets do affect yields, there-
fore, the insurance carrier may be allowed a grace period suffi-
cient to develop a premium-indemnity schedule which will reflect
the changes in yield probability.
6. Adapting Area-Yield Insurance
to All Crops in the Area
Area-yield insurance may be applied to all crops in an
area by allowing a farmer to include any crop in the insurance
program. A farmer could purchase, for instance, 400 acres worth
of insurance. This might cover his entire cropped acreage which
might be composed of a variety of crops.
Basing Insurance on Yields of One Crop
The farmer who applies area-yield insurance to all his
crops would want to know whether the insurance purchased would pro-
tect him against any or all crop losses caused by adverse crop con-
ditions. Whether it would or not depends on the nature of the cor-
relation existing between the crop used as the base and all the
other crops grown.
Let us suppose, for example, that wheat is the predominate
crop in an area and is grown on half of the acreage seeded to crops
in that area. The insurance carrier may develop a schedule of pre-
miums and indemnities based on records of wheat yields. An indivi-
dual farmer, for example, who plants 100 acres of wheat, 50 acres
of oats, 50 acres of barley, 50 acres of corn, 50 acres of sugar
beets, and who has 50 acres of pasture and 50 acres of miscella-
neous crops might insure.his entire 400 acres by paying the pre-
mium required to insure a certain level of wheat yields in the
area. His indemnity would depend on wheat yields in the area.
His problem may be stated: will the general crop conditions which
result in low yields for crops other than wheat also cause wheat
yields to be low in the area? The general answer would be affir-
mative but the correlation between yields would not be perfect.
Among the small grains, for instance, a high correlation would be
expected, but between wheat and corn, wheat and sugar beets, wheat
and pasture, the correlation would be lower.
This example suggest two other possibilities: (1) Area-
yield insurance might be based independently on two or more crops
in an area. (2) Premiums.and indemnities in an area might be based
on a weighted average of the most important crops in the area.
Basing Area-Yield Insurance on Two or More Crops
Area yield insurance might be sold on the basis of the
yields received for two or more crops in an area. In an area where
acreage is divided among orchards, truck crops, dairying, and small
grains, for example, the yield correlation among the crops might
be so low that if insurance was based on wheat alone, for instance,
the indemnities received would not correspond with poor crops of
fruit, vegetables, or feed.1 In cases such.as this normal fruit
yields might be calculated and area yield insurance could be of-
fered to fruit growers using the normal fruit yield as a base.2
Likewise some index of normal yield might be developed for truck
crops and area yield insurance sold to truck farmers on the basis
of this index. Area-yield insurance on the grains and feed grown
could be offered on a corresponding basis.
Basing Area-Yield Insurance on Weighted
Average of Crop Yield
Yields of the major crops in an area can be averaged and
the weighted average of these yields for any year can be expressed
as a percent of normal yield. A farmer could insure for some per-
cent of normal yield and the insurance carrier would calculate
premiums and indemnities on the basis of yield experience in the
area. A farmer would receive an indemnity whenever the index of
yields is below the level for which he insured. Insurance could
be sold on each of several crops, in such a case, and a farmer
could choose among them in any combination desired.
iThis condition is, probably, the exception rather than
the rule in American agriculture. Also we could argue that when
this condition is characteristic there is little need for crop in-
surance because (1) farmers' incomes would not be erratic because
of yield variations, and (2) crop insurance would not improve
resource utilization on the part of the firm.
2Normal yield is defined as the yield that would be re-
ceived in the area if weather conditions were normal. As before
it could be based on a moving average adjusted for trend and it
would be expressed as an index. When yields were normal, there-
fore, the index would stand at 100. When they were 90 percent of
normal, the index would stand at 90. A farmer buying insurance
could insure for yields of (say) 50, 70, or 80 percent of normal,
for instance. A range of premiums might be offered for insuring
anywhere from (say) 40 to 100 percent of normal.
The problem stated near the beginning of this chapter,
whether area-yield insurance could provide farms with adequate pro-
tection against crop failure due to adverse crop conditions and
whether it could work successfully according to the standards de-
veloped previously, can now be answered largely in the affirmative.
The reasons for this conclusion may be based on the fact that as
long as the average of yields in an area can be determined accu-
rately a normal yield expectation for the area can be developed.
This normal yield expectation can be refined by use of a moving
average adjusted for trend. The area yields can be used as the
actuarial data and farmers can be protected against the occurrence
of adverse crop conditions if areas are delineated so that there
is a high positive correlation between crop conditions faced by the
farmer and area yields.
The factors that appeared to work against the success of
all-risk crop insurance will not lead to adverse selectivity within
an area under area-yield insurance and will not endanger the suc-
cess of the area-yield insurance program. The insurance carrier
can be indifferent to the fact (1) that yields trend upward on some
farms and downward on others, (2) that yield deviations and coef-
ficients of variation are not the same on all farms in an area,
(3) that all farmers may not purchase insurance, and (4) that
farmers may insure only part of their seeded acreage.
We shall attempt in this chapter to construct and to test
a theory for crop insurance which is based on weather records. The
basic assumptions are (1) that certain meteorological phenomena
which are adverse to crop yields can be defined and are measurable,
and (2) that a schedule can be developed for an area which will
show (a) the premium required to insure against an occurrence of
these phenomena and (b) the indemnity which will be associated with
specific occurrences. The general formula for indemnities is de-
rived by noting the effect of certain weather phenomena on yields.
How this insurance might stabilize a farmer's crop income is demon-
strated by use of a selected case. We include a summary of the
relative advantages and disadvantages of this type of insurance.
1. General Concepts
The general concepts involved in weather-crop insurance
are: (1) the area, (2) the formula for indemnities, (3) the pre-
mium, and (4) the insured acreage.
The area should be of such size that weather in any season
would be fairly uniform throughout. Soil types and topography
IThe term "weather" as used in this case, and elsewhere in
this chapter, would include only those meteorological phenomena,
such as precipitation, temperature, and evaporation, which may be
used as actuarial data in the weather-crop insurance formula.
Damage from such phenomena as hail, flood, winter freezing, etc.,
if covered at all, would be treated as a specific risk to be
covered by riders or by special endorsements. The concepts of an
area developed in Chapter V would apply.
should be uniform so that similar weather would have similar ef-
fects on yields in different parts of the area.
The Formula for Indemnities
Some of the weather phenomena which are known to be impor-
tant in the determination of crop yields, such as rainfall and
temperature, would be selected on the basis of prior knowledge.
Regression equations, based on simple or partial correlations of
yields and weather data, would be used to indicate the normal re-
lationships between yields and weather and these would indicate
how yields might be expected to vary with variation in the phe-
nomena selected. These equations would be the basis for deter-
mining premiums and indemnities in the area.
The equation to be used in an area might be constructed
Yc = computed yields for the area,
Yg = normal area yield (as previously defined),
Xl, X2 X = selected weather variables expressed as the
difference between the observed value in any season and the respec-
a, b, n = regression coefficients measuring the amount
of change in yields associated with change in each weather factor
included in the weather-crop insurance formula.
Then the general formula could be written as follows:
(1) Y Y +aX1 + bX2 + nX.
Applying formula (1) to the case of a spring wheat area we
can employ the following definitions:
X1 = difference between the observed seasonal (May July)
precipitation and the mean seasonal (May July) precipitation,
X2 = difference between the mean observed maximum temperature
during the season (June July) and the mean maximum seasonal
(June July) temperature during a series of year, in degrees
X3 = difference between the observed preseasonal (August -
April) precipitation and the mean preseasonal (August April)
precipitation during a series of years, in inches,
a = regression coefficient for seasonal precipitation on
b = regression coefficient for mean seasonal maximum tempera-
ture on yields,
c = regression coefficient for preseasonal precipitation on
For use in the example, we have assumed the following
a = 1.5; i.e., each inch of seasonal precipitation increases
yields by 1.5 bushels per acre, ceteris paribus.
b = 0.5; i.e., each degree Fahrenheit increase in average
maximum temperature (June -July) decreases yields by 0.5 bushels
per acre, ceteris paribus.
c = 0.9; i.e., each inch of preseasonal precipitation in-
creases yields by 0.9 bushels per acre, ceteris paribus.
(The values for a, b, c, etc., would be established by
simple or partial correlation of the selected data, and these
values would vary from area to area.)
If Ya = 16 bushels per acre, and in a selected year X1 =
-3, X2 = + 2, X3 = + 2, then the computed yield would be:
Yc = 16 + 1.5 (-3) .5 (2) + 0.9 (2)
Ye = 12.3
If a farmer purchases insurance at the 100 percent level
he would be entitled, in such a case, to an indemnity equivalent
to 3.7 bushels per acre.1 A farmer insured at the 75 percent level
would not receive an indemnity because the computed yield was
greater than 75 percent of the mean yield.
.The values for;.meanyyield-tcould be.eliminated from the
equation by solving directly for the insurance indemnity. From
equation (1) cancel Ya and substitute for Y a value (I) which we
shall call the insurance indemnity.2 Then:
(2) I = aX1 + bX2 + CX3 + nXn
Using the same data as used above we may write:
I = 1.5 (-3) 0.5 (+2) + 0.9 (+2), I = -3.7
The indemnity, in case of 100 percent coverage, would be
3.7 bushels per acre.
Formula (1) or (2) might be appropriate in cases where it
is determined that the relationship between weather and yields was
found to be linear. In cases where the relationship is found to
be non-linear some modification of either formula might be appro-
priate.3 Formula (2), for instance, might be modified as follows:
iSince the insurance carrier bases the premium and indem-
nity on natural phenomena, price could be removed from the computa-
tion. Therefore, a set price of money value could be established
for a bushel, a pound, etc.
2The indemnity would be paid only when the value of I was
3We have concluded that the normal relationship is not
strictly linear. The marginal physical productivity of an inch of
rain, for instance, depends, in part, on how much rain has fallen
previously. In a semi-arid region, for instance, an inch of rain
in a "dry" year may affect yields much more than an inch of rain
in a "wet" year. Cf. Floyd E. Davis and J. E. Pallesen, "Effect of
the Amount and Distribution of Rainfall and Evaporation During the
Growing Season on Yields of Corn and Spring Wheat," Journal of Ag-
ricultural Research, LX (1940), 1-23. The normal relationship,
however, may be so close to a linear function that, within the
limits to which weather-crop insurance formulas may be applied, the
linear function might be the one that would find the most general
use. In the following studies it was assumed that the relationship
was a linear function or it was found that the use of a formula in-
volving only the first degree gave a good "fit" to the data. John
S. Cole, op. cit., pp. 8-24; George A. Rogler and Howard J. Haas,
op. cit., pp. 378-389; Ray F. Pengra, loc. cit., Fred H. Sanderson,
op. cit., pp. 769-776; A. L. Hallsted and E. H. Coles, op. cit.,
pp. 469-473; John S. Cole and 0. R. Mathews, loc. cit., A. L.
Halsted and 0. R. Mathews, op. cit., pp. 28, 36, and 41.
and n =
Then Im =
(3) Im =
For example, if f =
and n =
the modified insurance indemnity,
some function of I
some constant of power of I.
(aX1 + bX2 + nXn) f(In).
2, then using the data applied to formula (2)
m = (-3.7) (0.1) (-3.72)
Im = (-3.7) (1.369)
Im = -5.1
In real cases n would probably be less than 2 and a defi-
nite maximum limit would have to be established for Im.
The premium to be charged would be based on the indemnity
that would have been paid over some representative period providing
the particular type of policy had been in force throughout the
Three types of premiums could be offered: (1) equal annual
charges, (2) the net above a certain calculated yield, or (3) some
combination of (1) and (2). The choice among these types could be
made by the insured because the insurance carrier could be indif-
ferent about which type was used. The degree of stability (in
yields) desired by the insured might be the determining factor in
his choice. If relatively complete stability is desired, the farmer
might wish to pay a premium only in years when the calculated yield
is above the mean, as in the second option above. Less real sta-
bility would be obtained by the insured by use of the plan of equal
annual premiums, as in the first option above.
Insurance could be sold on basis of mean calculated yield,
i.e., an indemnity would be paid whenever calculated yield was
below the mean calculated yield. As an alternative, insurance
could be based on some percentage of calculated yield. Premium
rates would vary correspondingly.
The Insured Acreage
As in the case of area-yield insurance, the acreage to be
insured would not necessarily be bound by the acreage of crops
grown. In fact, weather-crop insurance would not need to be
measured in terms of acreage except for the need of preventing the
insurance from becoming a gambling device. The only requirements
of the contract would be that a farmer must commit himself to in-
surance prior to the period covered by the data used in the general
formula and that he would be limited to acreage under his control.1
If some of the data used in the formula are preseasonal precipita-
tion, say from August to April, for instance, then the deadline
for making the contract would be August 1 of the year prior to har-
vest. If no preseasonal data are used in the formula the deadline
could be moved forward to a date just prior to seeding.
2. The Construction of a General Formula
Since the payment of an indemnity to an individual farmer
would not be specifically determined by his yields or by the
general trend of yields in the area, the insurance carrier would
not be concerned about the level of the individual farmer's yields
or about the trends of yields in the area. We find it unneces-
sary, therefore, to make and to drop the assumptions presented in
Chapters III and IV. Actuarilly speaking, the problem will be
unaffected by the facts (1) that farmers grow several crops and
vary their acreage, (2) that only part of the farmers purchase
1How heavily he could insure each acre would be determined
by the average value of crops grown on such acreage. This would
be purely an arbitrary limit imposed to prevent a farmer from
insuring in excess of his insurable interest.
insurance, (3) that farm yields are not uniform, and (4) that
prices, technical and technological conditions change.
We can assume, however, that the insured farmer will be
concerned about the general relationship existing between his
yields and the indemnity which he may receive, which is determined
by measurements of the weather phenomena included in the insurance
formula. Although he may be certain that his premiums will equal
his indemnities (plus the administrative charges) over a long pe-
riod of time, we may assume also that the value of the insurance
to him will vary directly with the degree of inverse correlation
between his yields and the indemnities that he will receive. We
turn, therefore, to a partial appraisal of some correlations be-
tween yields and the weather factors which are known to influence
Precipitation and Yields
Soil m'oisture.--High and significant correlations have been
found to exist between soil moisture at seeding time and yields of
wheat (see Tables 9, 10, and 11). It has been suggested that such
measurements of soil moisture at seeding time might be used for the
purpose of predicting crop failure,2 for the purpose of constructing
tables of yield probabilities,3 or for the purpose of determining
the average relationship between yields and soil moisture.4
IThis appraisal must remain partial because the phenomena
to be explained are of a specific nature. No a priori argument
from general premises can tell us what the precise effects of any
general crop insurance formula will be. Consequently we cannot
prove that our theory is empirically valid but we can show impor-
tant discrepancies (if there are any) between our assumptions and
the observable phenomena. Cf. George F. Stigler, The Theory of
Price (New York: The Macmillan Company, 1946) Chapter I, Morris
R. Cohen and Ernest Nagel, An Introduction to Scientific Method
(New York: Harcourt, Brace Company, 1934), pp. 213-215.
2Hallsted and Coles, op. cit., pp. 469-473.
3Hallsted and Mathews, op. cit., p. 41.
Cole and Mathews, op. cit., p. 10.
CORRELATION BETWEEN SOIL MOISTURE IN THE SURFACE THREE FEET
OF SOIL AT SEEDING TIME AND YIELD OF WINTER WHEATa
Rotation Equationb Coefficient
Wheat follows: Winter Wheat Y = 3.12X 42.2 .807 + .021
Fallow Y = 2.51X 33.9 .458 + .034
Green Manure Y = 2.12X 25.7 .524 + .074
Barley Y = 4.31X = 65.2 .850 + .045
aBased on investigations made during the years 1910-1928
at the Fort Hays Substation of the Kansas Agricultural Experiment
bThe regression equation shows how
changes in soil moisture at seeding time.
bushels per acre, and X = percent moisture
of the soil at seeding time.
yields tend to vary with
We let Y = yield in
in the surface 3 feet
Source: A. L. Hallsted and E. H. Coles, "A Preliminary
Report of the Relation Between Yield of Winter Wheat and Moisture
in the Soil at Seeding Time," Journal of Agricultural Research XLI
PROBABILITIES OF OBTAINING SPECIFIED YIELDS OF
WINTER WHEAT WHEN THE SOIL WAS DRY OR WET
TO DESIGNATED DEPTHS AT SEEDING TIMEa
Depth to Failure 10 20 30
Which (4 Bushels Bushels Bushels
Soil Bushels or or or
was Wet or Less) More More More
Dry 27 in 38 7 in 38 0 in 38 0 in 38
or 71% or 18% or 0% or 0%
1 foot 18 in 53 23 in 53 10 in 53 0 in 53
or 34% or 43% or 19% or 0%
2 feet 5 in 34 21 in 34 11 in 34 3 in 34
or 15% or 62% or 29% or 9%
3 feet '6 in 61 51 in 61 43 in 61 14 in 61
or more or -10% or 84% or 70% or 23%
aData from measurements taken at
at Hays, Colby, and Garden City, Kansas,
bA foot section of soil was considered to be wet when 0.5
inch or more of available moisture was present, but under this
condition the soil was not necessarily filled to field capacity.
and Winter Wheat
A. L. Hallsted and 0. R. Mathews, Soil Moisture
with Suggestions for Abandonment, Kansas Agricul-
tural Experiment Station Bulletin 273 (1936), 41.
SUMMARY OF AVERAGE YIELDS OF SPRING WHEAT WHEN THE SOIL
AT SEEDING TIME WAS WET TO THE DEPTH SPECIFIEDa
Ydeld with Soil Wetu
to Depth of About
1 Foot 2 Feet i 3 Feet
Plot and Treatment or Less or More
A, Continuously cropped 6.3 11.7 15.5
B, Continuously cropped 6.7 11.7 15.9
C and D, Alternately fallowed 6.9 12.6 19.9
AvedigCge 6.5 11.9 18.2
aIncludes data gathered over a total of 765 crop years, at
15 field experiment stations over a period of some 30 years. The
study was conducted by the Division of Dry Land Agriculture,
U.S.D.A., and cooperating State agricultural experiment stations.
blf the second or the third foot contained only 3 percent
of available water in course-textured soils or 4 percent in fine-
textured soils, that soil section was not considered as being wet.
Source: John S. Cole and 0. R. Mathews, Relation of the
Depth to Which the Soil is Wet at Seeding Time to the Yield of
Spring Wheat on the Great Plains, U.S.D.A. Circular 583 (May 1940),
It has also been found that a high and significant correla-
tion exists, in some cases, between soil moisture in the fall and
forage yields, hay or pasture yields, in the year following.1 In
one study it was concluded that ". below average yields -of
forage can be predicted fairly accurately when the soil is dry
the preceding fall. With increasing quantities of moist soil in
the fall increasingly higher yields can be expected the following
season, on the average, but prediction is less accurate."2
1Rogler and Haas, op. cit., pp. 378-389. Correlation coef-
ficients of .72 and .74 were obtained for the correlation of forage
yield and soil moisture in the surface three feet and six feet, re-
spectively. Correlation coefficients of .80 and .84 were obtained
for correlation of forage yield with April-July precipitation plus
soil moisture in the surface three feet and six feet, respectively.
Ibid., p. 363. The regressions of forage yield on soil
moisture in the surface three feet and six feet, respectively,
Y = 183X + 160, Y = 111X + 127,
where X = inches of moisture and Y = yield of forage in pounds per