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The theory of crop insurance

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The theory of crop insurance
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Full Text
Peter E. Hildebrand Agricultural Econoniics
THE UNIVERSITY OF CHICAGO
THE THEORY OF CAOP INSURANCE
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
BY
HAROLD GRAHAM4 HALCROW
CHICAGO, ILLINOIS DECEMBER., 1948




PREFACE
In my study of literature prior to writing this dissertatalon, it became evident that the hope and approbation with which crop insurance was discussed had not been matched by the performance of any crop insurance program. Because of a general lack of theoretical analyses in the published works and because of a growing 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 dissertation.
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,.
Mvilton 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 manuscript. Several friends and colleagues aided me through discussions and correspondence.
The theory presented here may be of value in the development of future crop insurance programs. One conclusions, for instance, is that in theory the present Federal crop insurance program cannot succeed; but there is promise for successful crop insurance operation under plans for area-yield insurance and for weather-crop insurance herein described.
ii




CONTENTS
Page
LIST OF TABLES ... ... . e.. .. ..... . vi
LIST OF FIGURES . .. .. .. .. .. .. .. ... viii
Chapter
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'
Incomes
2. Effects of Yield Variations and of Yield
Uncertainty on Resource Utilization
Certainty
Time and flexibility Present and future technology Price certainty for factors and products
Uncertainty
3. Attempts to Establish Crop Insurance
Programs
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 Change
Base Yields for Farms and County Are Not the Same
All Farmers Do Not Purchase Insurance Farmers Grow Two or Nbre Crops
2. All-Risk Crop Insurance and Resource
Utilization
3. Conclusion
Appendix
V. AREA YIELD INSURANCE . ... .. .. .. 60
iii




iv
1. 0-6neral Concepts
The Area
The Normal Yield
The Current Yield The Insured Yield
The Premium
Insured Acreage
2. General Theory and Assmptions
Technical and Technological Conditions
Change
Mean Yields for Farms in the Area
Differ
All Farmers Do Not Buy Insurance
3. Effects of Area-Yield Insurance on
Resource Utilization
4. Illustrations and Criticism
5. Some Special Problems of Area-Yield
Insurance
Hail Flood
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
Mre Crops
Basing Area-Yield Insurance on Weighted
Average of Crop Yield
7. Conclusions
VI. WEATHER-CROP INSURANCE .............. .. 84
1. General Concepts
The Area
The Formula for Indemnities
The Premium
The Insured Yield
2. The Construction of a General Formula
Precipitation and Yields
Soil moisture
Preseasonal precipitation Annual precipitation Seasonal precipitation
Temperature and Evaporation
Summary
3. A Test Case
4. Summary of Advantages and Disadvantages
Advantages
Disadvantages
Conditions of Adaptability




v
VII. RECOMMENDATIONS APPLICABLE TO THE FEDERAL CROP
INSURANCE PROGRAM . . . . . . . * 115
1. Practices and Techniques
Area-Yield Insurance
Weather-Crop Insurance
2. General Philosophy and Procedure
3. The "Fixed Price" Amendment
4. Some Suggestions for Further Research
Development of Area-Yield Insurance Area delineation Normal area yield Premiums and insured yields Special problems Development of Weather-Crop Insurance Area delineation The formula for indemnities
Premiums and indemnities
5. General Conclusions
SELECTED BIBLIOGRAPHY . . . . ........ 129




LIST QF TABLES
Table Page
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 .. ... 6 & 12
2. Summary of Federal Wheat Crop Insurance,
1939-1936 a Z7
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,
Mbntana, 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 Mean Area Yield . . 72
7. Wheat Yields per Seeded Acre on Five Farms in Alton Community, Fergus County, Montanae . .e 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
vi




vii
14. Correlation Coefficients for Yield and
Precipitation for Four Crops in Three Areas of
Central South Dakota, 1919-1943, Inclusive . . . 96
15. Correlation Between Annual Precipitation and
Yields of Spring Wheat at Experiment Stations
in the Great Plains .* 97
16. Comparison of Estimated Yield with Actual Yield
for Stations in the Northern Great Plains . . . 98
17. Effects on Yields of Use of Weather-Crop
Insurance at Belle Fourche, South Dakota . . . . 110
18. Effects on Cash Returns of Use of Weather-Crop
Insurance at Belle Fourche, South Dakota . . . o 111




LIST OF FIGURES
Figure Page
1. Average eff eat 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 e 9 a & * a * & a 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




CHAPTER I
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 orcomplete 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 defined.
1. Purpose of Study
Crop insurance has been discussed for many years and numerous 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




2
what seems to be a peculiarly complex and difficult problem in
short-ran dynamics.
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 production plans,2 and changes in total output that do occur are largely
due to the incidence of weather and of disease or insects associated 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
lThere is evidence that corn-belt farmers expect the mean
of future yields to follow trends in past yields with small modifications for improvements in technology and varieties. See Theodore W. Schultz and 0. H. Brownlee, "Two Trials to Determine Expectation Models Applicable to Agriculture," Q_4rterly Jourr af'.Ecnoms, 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 insecurity in farmers' financial position. (3) Capital rationing, increasing risk, and lack of equity financing, combine to prevent expansion when a consideration of net marginal retun indicates expansion might be required to maximize net return. (4) The production 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 toward stability in total volume of products marketed. See Theodore
W. Schultz, Ariculture in an Unstable EconnfmZ (New York: itGraw Hill Book Company, 1945), pp. 10-45 and Sherman E. Johnson, Chanes in Farming in War and Peace, FM58 (Washington: United States Department of Agriculture, Bureau of Agricultural Economics, June 1946), pp. 64-69.




3
variation in some equitable manner among all farmers buying crop insurance.1
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 individual farmers' incomes are widely accepted as a desirable part
lCrop insurance should not be designed to protect a farmer against yield losses which are due to his own mismanagement, because to do so would tend to penalize one farmer and to aid another indiscriminately. Cf. Schultz, opcit., 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 necessary 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 Jb., pp. 902-911.




4
of agricultural policy.1 Harldship 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, therefore, 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 determining the probable effects of yield variations and of yield uncertainty on resource utilization by the firm, and (3) by reviewing some of the attempts which have been made to establish crop
insurance systems.
Chapter III presents the basic concepts of general insurance which may be considered in a program of crop insurance. A discussion is undertaken to determine how crop insurance programs should be developed to conform with these concepts.
In Chapters IV-VI we outline specific types of crop insurance programs. Three types or forms of crop insurance programs 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.cit., Chapter X, J. S. Davis "American Agriculture: Schultz' Analysis and Policy Proposals I The RevIew of Economic Statistics, XXIX (1947), 89-91: John D. Black "Professor Schultz and the C.E.D. on Agricultur~al Policy in 145,11Ju" g of Far Ea nomj isXII(16) 682,686; D. Gale Johnson, onc* Chapters XLI and XIII.




5
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 assumed, 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 insurance carrier does not have accurate knowledge of individual farm yields. This opens the analysis to the study of adverse selectivity among the insureds.1 The general effects of this type of crop insurance on intensity of cultivation, on cropping practices, 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 premiums 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 considered.
1Adverse 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. Aandehl., "A Crop Insurance Proposal," JoLaZ Science, Vol. I, No. 2 (August 1946), 12-13.




6
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. Indeinnities 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 agricultural policy which are related to crop insurance.
3. Some Definitions ad Assumptions
Crop insurance is defined as the insurance of crop yields, according to some measurement, against the effects of adverse weather. hs 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, respectively, 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,"l Journal of Farm 1Economics, XXV (1943), 759-776.




7
been defined by a certain group of writers to include expectations or anticipations which are based on a probability distribution having known parameters, and uncertainty has been defined to
include expectations or anticipations which are based on a probability 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 uncertainty does not depend on the fashion in which expectations
are '"catalogued." Rather, it depends on the effect of the phenomena described on the operation of the firm. It can be argued
that there is little reason for distinguishing between the operation 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, "Anticipations, Uncertainty, and Dynamic Planning,"Studies in Business 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 Contribution 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," Econometrc, IX (1941), 298-304; G. Tintner, "The Pure Theory of Production Under Technological Risk and Uncertainty," b pp. 306312.
2-bre specifically, Hart and Tintner have adhered to this definition of uncertainty while Knight ( pipb., pp. 233-234) defined 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 Compounding Probabilities," on. cit., p. 110 and G. Tintner, "The Pure Theory of Production Under Technological Risk and Uncertainty," op. cit., p. 305 and G. Tintner, "A Contribution to the Non-Static Theory of Production," o.cit., p. 92.
3See D. Gale Johnson, op. ctt., p. 38, Cf. Hart, "Risk,
Uncertainty and the Unprofitability of Compounding Probabilities," op, 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 produced and the factors expected to be used over the interval n' + 1, ns + 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, e ., 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 decisions 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, appears 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 distribution. 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




9
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 established require (1) that crop insurance cover major losses arising directly from Advsrmse eather phenomena, and (2) that premiums be made low enotx.k 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 indemnities, and vice versa, but they do require that adverse selectivity be eliminated and that losses due to bad management be separated from those due to weather.




CHAPTER II
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 variations on a farmer's income, (2) by determining the probable effects
of yield variation and of yield uncertainty on resource utilization 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.
2Marion Clawson, "Sequence in Variation of Annual Precipitation in the United States," The Journal of LTnd and Public Utility Economics, XXIII (1947), 271-287; John S. Cole, ogrretions Between Annual Precipitation and the Yield of Sri eat
in the Great Plains, U.S.D.A. Technical Bulletin 636 (1938); A. L. Hallsted and E. H. Coles, "A Preliminary Report on the Relation Between Yield of Winter Wheat and bMoisture in the Soil at Seeding Time," Journal of Aricultural Research, XLI (1930), 469473; John S. Cole and 0. R. Mathews, Relation of the Depth to which the Soil is Wet at Seeding Time to the Yield of Sprina Wheat on the Great Plains, U.S.D.A. Circular 563 (May 1940); A. L. Hallsted and 0. H. Mathews, Soil Moisture 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 AFronomy, 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.




11
the effect of yield variations on a farmer's income can be indicated 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 impacts of these variations might be counterbalanced in part by maintaining 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 an 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 income 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 resource 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
lFor another illustration based on county averages see
Carl P. Heisig, "Income Stability in High-r1isk Farming Areas," journal, of Parm Economicj., XXVIII (1946), 961-972. County data may not indicate the magnitude of the variations of yields on a typical farm.
2As shown by Timoshenko, o0- Cit., pp. 334-337.
3Cf. Heisig, loc. cit.




TABLE 1
YIELDS OF SPRING WHEAT AT BELIE FOURCHE, SOUTH DAKOTA, AND
COMPUTED INCOME EXPECTANCY OF A FARMER RECEIVING THESE
YIELDS, ASSUMING STABLE PRICES AND COSTS
li I
( Net Return
I Available for Net Return
I Family Living, for Management
Interest, after all
Gross Cash Income Taxes, Expenses
Year Yielda, Returnb Costs and Denpreciaticm and ChareSd
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 3,450 3.345 105 -2.895
Avg.. 17.5 I $8,747 03,857 I $4,890 1 $1,890
aAverage yields, in bushels per acre, received on 30 plots, with 5 plots on fallowed ground, 4 on green manured land, 12 following 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 Betyeen Annual Precipitation and the Yield of Spring Wheat in the, Great lains, U.S.D.A. Technical Bulletin 636 (1938), p. 6.




13
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 insurance,' 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, therefore, 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.
lDefinitions 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, oD. cit., pp. 62-71. Likewise there is evidence of low earnings by people employed in agriculture. See Theodore W. Schultz, on. cit., Chapter IX.
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. Cf. i1alton Friedman, "Lerner on the Economics of Control," The Jnurnal of Political Economy, LV (1947), 406. According to this definition it seems evident that resources in agriculture are not used in a manner to maximize their value, although it should be remembered also that yield and price variations and uncertainties are not alone responsible for this failure.




14
Certainty
A simplified theory of the firm based on single valued
anticipations can be constructed for conditions of perfect competition with the assumptions (1) that a definite price or series
of prices can be anticipated, (2) that there is a single known
production functions 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 factor 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
l1t 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 include 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 IT ar al, XLIV (1934), 60-67. Also it is desirable to assume that the entrepreneur maximizes satisfaction instead of profits, in this case, because profits are zero, which may be maximum, under perfect
competition.
2 This assumes perfect competition in the sale of the product 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. Diagrammatically, 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 marginal product of each factor must be equal to the marginal cost of the factor. These solutions may be generalized for imperfect competition in buying and selling by saying that the necessary condition for equilibrium is that the marginal revenue which may be attributable 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.




15
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
iSee J. R. Hicks, Value and Caital (Oxford University
Press, 1939) pp. 78-88 or J. E. Meade and C. J. Hitch, A__I.trgduction to Economic Analysis and Pol (New York: Oxford University Press, 1938), pp. 155-158.
2T. de Scitovszky has remarked that the assumption of profit 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, XaXIV (1944), 567-572. See also Frank H. Knight, Risk. Uncertainty, and Profi, op. ., 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 intended 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 programs of crop insurance. The approach is intended to be utilitarian. Thus it may be expedient to omit much of the general theory which is associated with price.




16
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 entrepreneural resource. 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 equilibrium would be achieved by fulfillment of the necessary and sufficient conditions.
The dynamic state introduces the idea of change. It becomes 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 considered 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
ISome writers have introduced the idea of the stationary
state, in part because it may be less exacting in its presuppositions. 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 consumption, 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 Politic-al Economy, XLVIII (1939), 305-327; A. G. Hart, "Anticipations, Uncertainty and Dynamic Planning," o pp. 25-27
and 56-60.




17
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 technoloey.--With certainty, both
present and future technical and technological conditions of production 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 discounting of future returns in comparison with current returns according to interest rates and time preference. Interest enters
into the calculation under dynamic conditions and becomes more important as expectations beccme more precise. Interest rates are relatively stable in agriculture, however, and the dual effects of
IKaldor, op. 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 Research 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 Mathematica Economics and Economerics, Lange, et al (ed.); on. cit., pp. 92-98; A. 0. Hart, "Anticipations, Business Planning and the Cycle," Quarterly Journal of Economics, LI (1937), p. 15.




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 substitution between outputs, (2) a diminishing marginal rate of substitution 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 certainty 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 different 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 certainty 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.
ISee Theodore W. Schultz, "Theory of the Firm and Farm Management Research" op. cit., p. 580.
2See Hicks, oD. cit.) Chapter XV (esp. p. 199) and mathematical appendix pp. 319-323, 325-326.
3This discussion follows Hicks, ibid, Chapter XVI.
41d., p. 210.




19
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 consequence 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 processing 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
Uncertainty
The assumptions given above are useful in outlining one
theory of the firm but they do not fit the situation which has confronted 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 conclusiono presented
elsewhere. Cf. D. Gale Johnson, "Contribution of Price Policy to the Income and Resource Problems in Ariculture,." 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 satisfactory explanation of profit we seem to be thrown back from the 'dynamic' theory to the certainty of the future, a condition of affairs loosely designated by the term 'risk' in ordinary language and in business parlance." See Knight, op. cit.,. p. 38.




20
factors, and (3) that production functions are multi-valued, with the greatest variation in vales 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 because 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 resource 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, oR. 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 Theory," The Journal of Political Economv, LV (1947), 450-458.
2proof of this statement was undertaken by Boulding in an analysis of the incidence of the profits tax. See Boulding, om. cit., pp. 567-572.
3M. Kalecki, Essays in the Theora of Economic Fluctuations (New York: Farrar and Rinehart, Inc., 1939), pp. 95-106. Some rationing could exist even with certainty because of the imperfections in the capital market, but rationing becomes more severe as uncertainty becomes greater. Eiuity 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 reactions to uncertainty. Insecurity of tenure often results in purchase 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.




21
The effect of rationing of the efficiency of the firm depends, in part, on the degree of substitution possible among factors. In agriculture, substitution among factors is common but there is also a general condition of factors acting in a complementary 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 coefficients, 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 plans.
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
1Cf. 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 ofI Orfect Competition (New York: The Macmillan Company, 1933), pp. 256ff., and R. G. D. Allen, Mathematical Analygis for Economists (New York: The Macmillan Company, 1939), Chapter XIX.
2This formulation follows 0. Tintner, "The Pure Theory of
Production Under Technological Risk and Uncertainty,' Econometrics, VIII-IX (1940-41), 305-312.




22
for a farmer to substitute a measurable cost for one that is largely 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 effects of risk aversion. The farmer may establish his scale of enterprise nearer the point of maximum profit. Being able to determine 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 of resources.
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 program was discontinued because of large underwriting losses, or (2) the program was continued only because the government (a) subsidized it and/or (b) made it compulsory. In no case has crop insurance 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 handled by private companies with limited resources, since crop losses can approach the magnitude of a calamity or a national catastrophe.1 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," Ant-rnaional Rpview of )Ericulture (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 Renomendations of the Presidentt a Committee on Cron Lnsurance, House Document No. 150, 75th Congress, First Session 1937, pp. 2-3.




23
first attempt of the United States Government to write all-risk
insurance.
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 Unsuccessful attempts were made to establish systems of non-compulsory crop insurance in Greece in 1927 and in France during 1929 to 1937.9
1Arcoleo, loc.cit. Transalted from Hemard, Theorie et
pratique des assurances terrestrea (Paris 1927), 1st part, p. 213.
21bhid. Translated from Lans-Stauffer and Rommel, Elementars;haden and Versicherung (Born 1936), Vol. 1, p. 112.
3Thid., p. 274E. Translated from Rommel, TL'asstirance
contre la Pelic, reprint from the Revue Generale des assurances terrestres, No. 1, 1938.
4ai. Translated from Lans-Stauffer and Rommel, on. cit., Vol. 1, p. 87.
5M. Hilderbrandsson, "Insurance of Mbteorlogical Risks,"
International Review of Aericulture (Rome: International Institute of Agriculture, 1924), pp. 137-138.
6See Report and Recommendations of the President's Committee on Cron 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, 22-25.
8Arcoleo, opn. cit., p. 274E.
9Ibid. p. 309E.




24
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 Council, 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 payment 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. 2bther.4ell, "A
Study of Crop Insurance," Report of the Sgkxtnhawan Reconstrucn i I Appendix 3 (Regina, 1944); Manitoba Economic Survey
Board, "Crop Insurance in Manitoba: A Reort on the Feasibility and Practicability of Crop Insurance in Manitoba" (Winnipeg 1940 mimeographed); Anarew Stewart "Crop Insurance in Alberta" tUnpublished Re ort, Alberta Post-War Reconstruction Committee,
monton, 19M5 Andr6w Stewart, "Stabilization of the Income of the Primary Proaucer," Canadian Journal of Economics and Political Science, XI (1945), 359-372.




25
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 companies to write insurance covering more than hail were short lived. One attempt was made in 1899.2 The next was in 1917 but the companies lost about $200,000 on the venture.3 In 1920 several companies sold some crop insurance but one company alone lost about 1.7 million dollars.4 Again in 1930-31 and in 1937 mutual companies 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 Corporation7 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 Saskatchewan paid $6,452,763 and received $28,999,711. Manitoba farmers paid in 41,910,211 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, op. cit., pp. 43 and 44.
2Coneressional Digest, December 1936, p. 292.
3C. L. Rogers, "Crop Insurance," Conference Board Balletin (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, op. 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.




26
restricted to wheat, covering the 1939, 1940, and 1941 wheat harvests. 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 harvest. From 1945 through 1947 wheat, cotton, and flax were insured on a nation-wide basis. The 1947 amendment to the Federal Crop Insurance 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 commodity, whichever was smaller.
A financial summary of federal wheat crop insurance is presented in Table 2. A statement of the Senate Committee on Agriculture and Forestry on crop insurance experience is as follows:3
The Federal crop-insurance program can best be characterized as an experiment. Up to 1947, the losses incurred
in the operation of the act had consumed $90,000,000 of
the 100,000,000 of capital provided for the Federal crop
insurance in addition to current appropriations to meet
operating costs. Appropriations for the current year provided for putting the crop insurance activities on an experimental basis in order to help develop sound principles
for conducting crop-insurance programs. The 1947 cropinsurance program for wheat showed a substantial profit
owing to the exceptionally good crop over most of the
wheat-growing region.
IInformation on crop insurance during 1942 and after is
from various issues of the Apricultural. Finsnoe eview (Washington United States Department of Agriculture) and from Report of the Mansper of the Federal Crop Tnsuranoe.Corporation, 1947 (Washingtton: United States Department of Agriculture, 1947).
2See 80th Cngress, 1st Session, Public. Law 320 (S. 1326), p. 1, Sec. 508(a).
3See 80th Congress, 2nd Session, Long-Ranee Agricultural Policy and Program. Report of the Committee on Aericulture and Forestry, United States Senate (Report No. 885, February 9, 1948), p. 66.




27
TABLE 2
SUMMARY OF FEDERAL WHEAT CROP INSURANCE, 1939-1946
Total Percent
U.S. of
Acreage Seeded U. S. Premiums Indemnities Percent of
Ineur6d Acreage Seeded Collected Paid Indemnities
(1,000 (1,000 Acreage (1,000 (1,000 Covered by
Year ares acres) nsured 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 Statisti e~. 6 (Washington: United States Government Printing Office), p. 7, A rioultal Finance Revigyw, IX (1946), 110; Report of the Man~er of the Federal Crop sura~oe Corporation, 1947, o_. cit., p. 11 and The Wheat iaS(Washington: United States Department of Agriculture, September-December 1947), p. 10.
The results described above have been considered by many
to be disappointing. At the same time it may be generally recognized that the case for crop insurance is strong and that eventually 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.




CHAPTER III
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 cerrier agrees to make good any financial loss an insured may suffer within the scope of the contract 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 mathematical 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 crcp insurance should be written and (2) to suggest means for dealing with the problems which are peculiar to insuring crops.
Some of the guildes which have been accepted are as follows:1 (1) The insured should have an insureble 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
1For further discussion see Robert Riegel and Jerome S. Miller, Insurance Princinles and Practioe, 3rd ed. (New York: Prentice-Hall Inc., 1947), Chapter II. See also John H. Maude?,
General Insurance, 3rd ed. (Chicago: Richard D. Irwin, Inc., 1947), Chapter IV; Francis T. Allen, Gen(ral Prinr-iples of Insurance (New York: Longmans, Green and Co., 1941), Chapter I.




29
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 Ihauranbie 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."' In property insurance, the doctrine of insurable interest rests on the principle that insurance 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 gambling, and it should not be public interest to assist in the collection of gambling gains; and (2) without insurable interest a person would be encouraged to bring about the very contingency insured against.
The nature of the insurable interest may be defined in the policy. In most insurance policies covering an interest in property 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 contingencies.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.




30
The extent of the insurable interest is generally determined by the amount of loss that will be suffered by the insured if the event or contingency insured against actually occurs. Yost insurance policies, however, do not cover the full insurable interest.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 of loss3
Standard concepts of insurable interest must be modified, however, when consideration is given to the problem of insuring crops. A farmer's insArable 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 .ntereei 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 insured level of yield, as in the case of the all-risk insurance defined above. In some other instances the insurable interest of the farmer has been defined as his investment in the growing crop.5
1See ibid.
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, or. cit., pp. 270 and 434.
3kh:A., p. 434
4See Rogers, on. cit., pp. 81-83, Conprpsional Doest, 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 inaccuracies in farmers' reported costs, and (2) because price declines 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 Reort of the Manager of the Federal Cron Insura=ce Corporation, 1947, on .cit., pp. 25,30.




31
T-n nwI other cases attempts have been made to reduce the carrier's liability by restricting the yield coverage to a level not exceeding the average investment in the crop at time of abandonment of the crop.1
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 insurable 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 indemnity 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, therefore, 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
1 The 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. 1p 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, ibdo 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 conditions under which an indemnity may be paid. See Magee, o~ i.
pp. 356-358.




32
Yield expectations are influenced by farming methods and
by investments in the crop. Furthermore, crop investments are influenced by price and market expectations as well as by yield expectations. Actuarially speaking, however, the probability of indemnity must not be influenced by action of the insured if adverse 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 Ls 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 chapter 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 farmer's insurable interest, as previously defined, is dealt with by assuming that there is a positive and highly significant correlaation 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," Jottrnnl of Land and Public Utility Economics, XVI (1940), 277.
2This assumption is reviewed in Chapter V.




33
crop condition faced by the farmer can be insured by insuring area yield. Since a farmer's yields will depend on crop conditions experienced, 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 position to benefit from an adverse crop condition, various limitations are considered as to the amount of insurance he may be able to purchase.
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 payment 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 specific data.
iThis may be true providing the area is delineated as suggested 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, on. cit., Chapters XIV, XV, XXXI, and Francis T. Allen, Chapter XIII.




34
3. The Cost of Cron Insur ace
The third rule or guide stated above is that the cost of
insurance must not be prohibitive. We may assume, as a first approximation, 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 administration,1 or (b) by obtaining a large number of risks and by efficient
N
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 Corporation, for instance, the following reasons were given for not buying insurance:2
"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."
1 As 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,"
op. Ct., p. 258. Clendenin cited the reasons as being typical.




35
"The policy wontt 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 highrisk area, when the use of insurance may commit a farmer to a fairly 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 certainty than would some other farmers, e.g., those in a low-risk
2
area.
'In another investigation it was concluded that participation 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 Sumary of Report of the Whegt Crop Insurance Consultin C0ommittee-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 assume that there is for every individual a preference function or rather preference functional which vill depend on the probability distribution mentioned." See Gerhard Tintner, '!A Contribution to the Non-static Theory of Production," Studies in 3Mthematical EconomLcs and Econometrics, Lange, at. ed. (Chicago: The University of Chicago Press, 1942), p. 107.




36
Another possibility that may cause a cost to seem prohibitive, in case of all-risk crop insurance, is that a farmer may be optimistic about his yields.1 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 individal 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 because (1) a large number of risks reduces the average administration 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 numbers. These rules find an application in crop insurance.
Administrative expense is a matter for empirical rather
than theoretical verification. We may merely illustrate how expenses 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
1This 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 ran of poor crop years, the case of risk being applied to any crop yield probability, or to any crop condition probability, in any year.
3Hart, i n. p. 116.




37
acreage was insured. The average cost per bushel was about twothirds as high where 40 percent of total acreage was insured as it was where 17.8 percent was insured (see Table 3).
TABLE 3
TYPICAL OPERATING EXPENSES OF THE FEDERAL CROP INSURANCE CORPORATION UNDER CONDITIONS ASSUMED Assumed percentage of
acreage insured
ARA 17.8 1 30.0 kO.0 i 17Q8J .0 40.0
Operating expenses Operating expenses
.......... n !per premium bushel noer protected bushel.
United States average $.33 $.24 $.21 $.031 $.023 $.020 Ohio Valley state .67 .49 .42 .036 .026 .022
Northern state .55 .40 .35 .041 .030 .026
Western Great Plains wea .22 .16 .14 .038 .028 .023 Pacific Coast state .33 .24 .21 .019 .014 712
1 1
Source: C. L. Clendenin, "Federal Crop Insurance in
Operation," Weat Studies of the Food Research Institute, XVIII (1942), 269.
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
1Total 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, oR. 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, o c., 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, ct., p. 39.




38
of farms, geographic areas, and crops covered by insurance increase, 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 reduce unit administrative costs and to improve the distribution of
losses; bat large numbers alone will not guarantee that losses will
be equal to indemnities in any one year.
5. The Mthematical qaalcalation 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
1Favorable 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 experienced a production revolution during the war years. And a large part of the change is irreversible." Quoted from Sherman E. Johnson, oD., 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 communication the insurance of overdue ships lostt 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 very 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.




39
common premium rate will apply to all risks with similar probabilities 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,l 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 premiums 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 reserve 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 serveral 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,.
1Sebelow, Chapter V. part 1.




40
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 conditions, 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 harvesting a poor crop, plus the loss necessitated by the delky 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 occurrence of a single event.
Von Neumann and iorgenstern pointed out that in utilizing a group of physical variables to maximize satisfaction "sometimes uncontrollable factors also intervene, e.g., the weather in agriculture. These, however, are purely statistical phenomena. Consequently 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 Mrgenstern, 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 conditions, such as new varieties, improved techniques, etc., are anticipated or are realized,
2Cf. T. A. Kiesselbach, Arthur Anderson, and W. W. Burr,
The Seedbed Factor in Winter Wheat Produntion, Nebraska Agricultural Experiment Station Bulletin 228 (1927).




41
The solution for crop insurance must be based (1) on the
recognition that such petuliarities do exist and (2) on a def~inition of what we wish crop insurance to accomplice. 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 adverse 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.




CHAPTER IV
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 and undertakes to determine whether such insurance can work successfully, according to standards developed above.
1. The General Theory and Assumntions
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 insuring for 75 percent of the base yield. It was assumed, apparently, 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 purpose 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




43
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 technological 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 mast 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 advance, 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 assumed 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 farzi 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., indemnities 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 paymeats. 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




4
yield. Considering the general conditions of increasing riski
and capital rationing which we find in agriculture, it may be concluded 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 8 priori 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 openpollinated varieties. The percentage increase is usually about the same on good as on poor land ..
iThe 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 entrepreneur should be indifferent to increasing risk only if he has an unlimited capital budget. Such a situation is seldom found in agriculture.
2Cf. Hart, "Risk, Uncertainty, and the Unprofitability of
Compounding Probabilities," opt. cit., n. p. 116 and F. H. Knight, op. cttv 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), i.946 Report on Postwar Aprieultgra1 Policies (79th Congress, 2nd Session, House Report No. 2728).
4The following data on yields are from Sherman E. Johnson,
cit., pp. 26-36, except where otherwise noted.




45
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 instance, ,... New varieties of oats have been introduced that result in increases comparable to those of hybrid corn in yields per acre o .." 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 1942-4 than in 1935-39,
with a planted acreage only four-fifths as large . Back of this increase are improved varieties, soil and moisture-conserving practices, and mechanization which increases the timeliness of operations "
"The continued increase in yields of cotton can be attributed largely to the following factors: (1) increased use of fertilizer, (2) a shift to higher yielding areas with reduction in
acreage, (3) careful selection of land within each area cnd on
lTo new varieties of barley, Compana and Glacier, developed cooperatively by the Mntana Agricultural Experiment Station and the United States Department of Agriculture, have consistently outyielded older varieties. See S. G. Litzenberger, oaa and Glacier Barley, Mntana Agricultural Experiment Station Bulletin, 422 (Bozeman, Mntana, 1944), pp. 7-11.




46
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 increased 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 conditions change on individual farms, it can be shown that the farmers with increasing yields wouId find that the flat premium rate would make the sum of premiums for 15 6r 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
1This method was proposed by T. J. Reed, See T. J. Reed,
"Crop Insurance to Stabilize Wheat Growers' Incomes," unpublished MS. Thesis, Iowa State College, Ames, Iowa, 1947.




47
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) premium 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 operations 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 &0ntana, 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," gn. 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 b'lance 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 reduction in his current premium rate. (2) When a farmer had five consecutive years without indemnity excluding 1944 when no insurance was offered, he could receive a ten percent reduction in his current premium rate. A wheat or cotton farmer carrying insurance could select either one of these plans in 1946, but the plans were restricted to wheat in 1947. See APricucltural Finance Review IX (1946), 72.




production for each farm. With the adoption of county premium rates for cotton in 1946, all crops in both the permanent and trial pro~ams usually are insured under uniform
county-wide rates. Higher rates are charged on certain
'high risk" farms in a county.1
TABLE 4
CLASSIFICATION OF 1269 FARMS IN CHOUTEAU COUNTY, MONTANA,
ACCORDING TO AVERAGE WHEAT YIELDS 1925-1932
Average Yield Bushels Number
Per Acre of Farms
0.0 2.5 ... ........... ...52
2.6 5.0 ... ........... ..160
5.1 7.5 .... .......... ..231
7.6 10.0 .... ....... ....265
10.1 12.5 .. .. ... .. 190
12.6 15.0 .... .......... .130
15.1 17.5 ... .......... .. 74
17.6 20.0 ... ........... ...52
20.1 22.5 .... .......... ...33
22.6 25.0 ... ........... ...31
over 25.0 ... ......... .. 51
Source: Data taken from records in Chouteau County P.M.A. office at Fort Benton, Montana.
TABLE 5
COUNTY PREMIUM RATE, AVERAGE BASE YIELDS AND AVERAGE INSURED YIELDS, IN CHOUTEAU COUNTY,
MONTANA, FOR 1947, IN BUSHELS PER ACRE
WINTER WHEAX SPAINU WHEA
Sunmr jCont inuous Sumimer Continuous Fallow Crop Fallow Crop
For 75% of base yield i
insured:
Premium rate,
county-wide 1.8 1.4 1.8 1.4
Average base yield 8
for county 16.3 11.1 14.3 9.1
Average insured yield 1 8
for county 12.2 8.3 10.7 6.8
For 50% of base yield
insured:
Premium rate, 6
county-wide .7 .6 .7 .6
Average base yield .
for county 16.3 11.1 14.3 9.1
Average insured yield for county 8.2 5.6 7.2 t 4.6
Source: Data obtained from records in Chouteau County
P.M.A. office at Fort Benton, Montana.
AaTicUltural Finance Review, IX (1946), 71. Underlining




49
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 1, 2, . n.
For example suppose: y1 + 5,Y2 =- 4, Y3 = 6,
7, and y5 = + 12; xa = 12, b =16; 3/4Aa 9, and 3/4Xb = -- Indemnities would be as follows:
Farm A = 0 + 1 + 3 + 4 + 0 = 8 bushels per acre for the
5 years.
Farm B = 0 + 0 + 2 + 3 + 0 = 5 bushels per acre for the
5 years.
2This may be demonstrated (as in previous footnote): Let Xa, Xb, . and Xn be mean yields; let 3/i1iRa, 3/4.Xb, . and 3/45Xn be respective insured yields; and let the variation in yields be yl (cRa), yj (kb), y y(Xn); y2 (Xa),_y9 (Xb), 3
(An) ; ... and yn (Ra): Yn X) n
For example suppose where Xa 12 and Ab = 16 that yl = + 40%, y = -40%, Y3 = + 60%, y4 = 60%, y5 = 0. Indemnities would e 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.




so
order for there to be no inherent incentive for an adverse selectivity 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. 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 situations may develop: (1) Some farmers may decide that the mathematical 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 insurance 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
lGiven a number of farms A, B, .. N, deviations of yields on these farms, in years of indemnity, would have to be
- 1/'4Xa, l/4IXb, . ,- l/4Rln minus some constant x which would be the same for each farm.
2 The data below are from a study conducted at 14i experiment stations in the Northern Great Plains during the years 19061935 and the data refer to yields per acre of spring wheat:
Eight high yielding stations: AR 16.87 10.83 C.V. = 6.Y
Five low yielding stations: = 11.89 6- = 8.89
C.V. =748
See John S. Cole, op. cit., pp. 26-28.




51
for (say) three, five, or more years, and by setting the deadline for purchase far'enouigh 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 selectivity should be greatly reduced. One of the difficulties with setting the deadlines far enough ahead is that farmers may sometimes 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 experience 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 conditions 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 insurance at rates which disregard the additional hazard, (2) to establish 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 19146 the Federal Crop Insurance Corporation 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 because seedbed conditions were good and premium rates and insured yields were based on previous drought conditions. See Clendenin, ibid, p. 254.




52
is known to exist. If premium rates are set to disregard the occasional additional hazard the insurance carrier will be subsidizing 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 selecti vity 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 famrs 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 maintain the scale of enterprise in these instances. Under these conditions 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
lwe 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.
2 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.




53
crops may be substituted for insured crops, or insurance may be dropped.
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 relationships of a farers 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 insurance 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 possibility 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 return for management (1) if there is a complete crop failure or (2) if crop conditions are very favorable. The farmer would prefer,
'With 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 maximizationi, therefore.
2 The 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
premiums are equal to the insurance indemnity.




54
therefore, that the crop would be a complete failure1 or that conditions 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 tendency 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
program.
lOne 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 Fon the insured farm] represents generally more protection than the investment 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, 1st Session, Public Law 320 (S. 1326), p. 1, See. 508(a). For a discussion of the reasons.:for this amendment see 80th Congress, 1st Session, Department of Agriculture Appropriation 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 experimental 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 additional hazard. In 1947 the F.C.I.C. was limiting coverage on tobacco to 75 percent of the average investment, or to about twothirds 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.




55
The general effects of all-risk crop insurance on resource utilization by the firm may now be summarized. (1) When yield expectations are relatively poor, all-risk crop insurance will encourage 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 indemnities. Crop prospects could not become bad enough to discourage seeding as long as.-probable value of the insurance indemnity 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 return 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.
3. Conclusion
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 downward, 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




56
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, regardless 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 farmers with relatively good yield expectations compared with their insured yield woul4 mindmize'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 farmers would tend to insure more heavily when yield prospects were poor.
4I. 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 insurance indemnity less qualifying input (costs), the use of allrisk 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 insured yields, inputs may be minimized to the level which is necessary to qualify for crop insurance. When yield expectations are




57
very poor, however, the continuation of minimum inputs to qualify for crop insurance may be encouraged because the insurance indemnity 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.
Appendix
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 proportionately, 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,1 and (2) that the correlations 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 could1.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 correlated 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, 1400-4LI01, '427, 48.1-482, and '499.
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,"t Journal of Farm Economics, XXVII (19145), 770-772.




58
future, help to reduce the more violent of the price fluctuations which have been due to yield variations. 1
When stated as above, the argument is rooted in empirical data and, therefore, the answer derived will be of limited, although perhaps valuable, application. Using an a priori argument, however, if the crop yield on any individual farm bears no particular or consistent relationship to the, nat-ional 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 the country. 3
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 insured 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., Chapters 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 agricultural 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.
3 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 Agricultu.,al Experiment Station, Research Bulletin 321 (Ames, Iowa, 19413), pp. 9 and 10, and DJ. Gale Johnson, Forward Prices for-Agriculture, op. cit., pp. 233-24..




59
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 commodity insured.




CHAPTER V
AREA-YIELD INSURANCE
A basic assumption underlying the theory of area-yield insurance 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 premium 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 previously developed.
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 insured yield for the area, (4) the area yield in any one year, (3) the premium, and (6) the individual farmer's acreage which is to be insured.
60




61
The Area
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 experienced in a season would have a similar effect on yields throughout 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 delineated 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 Station Bulletin 213 (Storrs, 1936); F. F. Elliott and R. H. Rogers, Types of Farming in South Dakota, South Dakota Agricultural Ex- .L,. periment Station Bulletin 238 (Brookings, 1929); F. F. Elliott, tesse 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 Michigan, 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 Station 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 Agricultural Experiment Station Bulletin 342 (Lafayette, 1930).




62
Type-of-farming areas should be divided in some cases where
1
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 contitions faced by
any farmer in the area. The size and shape of the area would be
2
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
area.
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 Adjustments 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, mimeographed).
2The main ecological factors to be considered are water relationships, temperature relationships, light relationships, and the form and availability of crop nutrients. These determine the physiological limits of crop production. Some geographic and economic 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 developed. All of the above factors have been discussed under the title of "ecological crop geography." See K. N. W. IUlages, Ecological Crop Geography (New York: The Macmillan Company, 1942), Chapters I and IX.




63
the mean area yield that would be realized if crop conditions were "normal."'l A moving average adjusted for trend might be "practical" 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 estimate 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 insuring that current area yields would be equal to normal area yield or to some percentage of normal'yields. If a farmer chose to insure normal yield he would be eligible for an indemnity any time
1This 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-I.34.6. 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 = 14J.5 bushels per acre; mode = 13.2 bushels per acre; and median = 14l.0 bushels per acre. See Agricultural Statistics 19416. op. cit,., p. 7.
2The same method could hot 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 adjusting 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.




64f
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
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 per acre.
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 tun methods could be made by the farmer buying the insurance contract.
Insured Acreage
The individual farm acreage to be insured would be determined 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




65
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 indemnity.
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 percent 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 preclude the seeding of a sufficient acreage in a given year to establish 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 allotments for the production control program used in the United States in the 19301s. (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




66
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 downward. 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 4I). 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 protected 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 significant,1 farmers may be protected against yield variations by insuring their seeded acreage providing that the variations among farms are similar in bushels
lThis 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, because a lack of correlation might be due to the farmer's own farming practices.




67
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 idealal? 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 [40O 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 assumption, 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
to: seeed crege)x (ian vield of farm x C.V. of farm yield
to:a (seeyceg)~ield ofN oraeaxx
Using the above figures as an example in the formula the acreage to insure would be as-follows: 40 (150 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 insurable 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 relat're 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 individual farms do not differ to any marked degree, justice could be obtained 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 farmers buy insurance within an area, because all premiums and indemnities are based on area yields. As discussed previously, however, farmers may be able to estimate area yields a year or two in advance 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. 1Actually it may be greater or less than unity and farmers
'Hicks used the term 'elasticity of expectations' as t'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




69
may be well aware of that fact. Consequently they might buy insurance heavily when yields are expected to be lower than the formnula 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 refundta.ble. (2) A long-term contract, a three, four, or five-year contract for instance, with early deadlines for application 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 current yield expectations, the use of area-yield insurance may contribute 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
'We 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.




70
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 consistent with th e 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 physical 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 homogeneity 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




71
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 insured 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 presented 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 significantly increase yield stability under the conditions illustrated. 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 optimum conditions that could be established for an area-yield insurance 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.




72
TABLE 6
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 I 24rea
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
194 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
Average
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 14.6 16.6
1945 16.0 19.9 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
Average I
Deviation 1.9 1.5 2.1 1.7 1.8
Source: Data on yields were gathered by Department of
,;r,,~f, ,n l.nnnnmi- r T(nn.qn:R R-"n'f'r n11Po'r,_ Manhn'ttan- Kansas




73
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 41.6 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.
TABLE 7
WHEAT YIELDS PER SEEDED ACRE ON FIVE FARMS
IN ALTON COMMUNITY, FERGUS COUNTY, MONTANA
Year Area A i Area B
1930 17.8 17.8 j 10.0 10.0
1931 j112.0 12.0 6.7 7.1
1932 1 538.3 .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 I12.5 5.5 6.0 17.0 12.8
1938 27.5 20.5 22.5 23.5 27.5
1939 13.4 141.3 14.3 13.4 14..2
19410 j13.4 13.5 13.0 14.1 22.4
19141 15.8 13.0 13.2 11.9 16.1
1942 16.9 14.0 13.0 13.7 16.7
1943 18.8 j15.7 114.0 14.7 18.0
19414 114.1 15.5 15.3 114.2 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
allail damage.
bDeflated to 1930-19146 base.
cM1l farmers insure on basis of area yield.
Source: Data obtained from records in Fergus County P.M.A. office at Lewistown, Montana.




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TABLE 8
WHEAT YIELDS PER SEEDED ACRE ON FIVE NORTH DAKOTA FARMS
Year Counties, Area A Counties, Area B
Dickey Dickey Mountrail Divide Williams
1923 5 6 10 17 21
1924 is 10 11 21 20
1925 16 14 25 20 23
1926 4 7 9 18 17
1927 10 13 10 17 1 25
1928 16 12 24 24 0
1929 13 12 12 17 15
1930 15 14 4 is 8
1931 7 9 0 0 0
1932 13 13 is 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
Source: Unpublished material of Farm Credit Administration, St. Paul, Minnesota.
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 consistent 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 insurance. 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 variations that may be tolerated in delineating areas.




75
and may not be paid sometimes when his yields are below his-average. 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 conditions which the insured may face are insured rather than the outcome 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 conditions and to avoid insuring those caused by variations or mistakes in management. The above criticism lacks content, therefore, when it is applied to the actuarial features of area-yield insurance, 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 indemnities and low yields is inconsistent some undesirable income effects may result.
S. 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




76
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.
Hail
Insurance against damage from local hail storms might be obtained by attaching a hail rider1 to the regular insurance contract 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 double 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 warranted.
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
'The rider would apply only in case damage was not uniform over the area. The cost of this rider vould 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 Insurance for Montana, has stated, "I am still very reluctant to conclude 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?"t, Montana Farmer-Stockman (June 1, 194.7), p. 39.




77
no indemnity. (3) If, prior to the hail storm, indicated yields were below normal in the area (or if yields in the non-hailed section 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 F1~C1
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 inactirn:, 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
lThe total indemnity may be calculated as follows:
Let I =total indemnity,
Yi = insured yield,
ha = indemnity due from area-yield insurance, and percent hail damage.
Then Yji I a= balance of crop left after area-yield
indemnity is calculated and I = Ia + h (Yi Ia)-




78
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 inffestation is general over an area no
special problem exists and the usual provisions of the insurance contract would provide a compensating indemnity. When the infestation is localized in one section of an area, however, a peculiar problem would exist. 1Where 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
1The relative economic importance of local insect infestations 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 19145 and 194.6, Montana Agricultural Experiment Station BulleTin 44.2 (194.7), pp. 4-18.
.21f 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.




79
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 response 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 restricted in the speed and extent to which they will alter production 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
lCf. 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 product prices.
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 costprice situation. Cf. John M. Brewster and Howard L. Parsons, "Can Prices Allocate Resources in American Agriculture?"t, Journal of Farm Economices, XXVIII (19416), 938-960, and D. Gale Johnson, Forward Prices for Agriculture, op. cit., Chapters V and VII.




80
(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 relationship, the carrier should be able to state a normal area yield as accurately as can the farmer who is faced with the decision of insuring.
While the effect of market changes on yields may be considerable, the importance of the above problem to the success of area-yield insurance should not be exaggerated. In actual operation, the insurance carrier may quickly detect the presence of an adverse selectivity among areas by comparing premiums and indemnities between areas with the relative percentage of farmers purchasing insurance in different areas. Furthermore- it generally requires two or three seasons for market changes to have much effect on yields. In cases where markets do affect yields, therefore, the insurance carrier may be allowed a grace period sufficient to develop a premium-indemnity schedule which will reflect the changes in yield probability.
6. Adapting Area-Yield Insurance to All Crops inthe 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.




81
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 protect him against any or all crop losses caused by adverse crop conditions. Whether it would or not depends on the nature of the correlation 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 needed to crops in that area. The insurance carrier may develop a schedule of premiums and indemnities based on records of wheat yields. An individual 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 SO acres of miscellaneous crops might insure.Ms entire 400 acres by paying the premium 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 affirmative 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) Areayield 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




82
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, oi feed. 1 In cases suchas this normal fruit yields might be calculated and area yield insurance could be offered 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 percent 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.
lThis 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 insurance 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.
2 Normal yield is defined as the yield that would be received 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, therefore, the index would stand at 100. When they were 90-pe.:rceht 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.




83
7. Conclusions
The problem stated near the beginning of this chapter,
whether area-yield insurance could provide farms with adequate protection against crop failure due to adverse crop conditions and whether it could work successfully according to the standards developed 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 accurately 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 success 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 coefficients 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.




CHAPTER VI
WEATHER-CROP INSURANCE
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 derived by noting the effect of certain weather phenomena on yields. How this insurance might stabilize a farmer's crop income is demonstrated 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 premium, and (4) the insured acreage.
The Area
The area should be of such size that weather1 i any season would be fairly uniform throughout. Soil types and topography
'The 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.




85
should be uniform so that similar weather would have similar effects on yields in different parts of the area.
The Formula for Indemnities
Some of the weather phenomena which are known to be important 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 relationships between yields and weather and these would indicate how yields might be expected to vary with variation in the phenomena selected. These equations would be the basis for determining premiums and indemnities in the area.
The equation to be used in an area might be constructed as follows:
Yc =computed yields for the area,
Y= normal area yield (as previously defined), X1, X2 . Xn = selected .weather variables expressed as the difference between the observed value in any season and the respective mean,
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 c a + aX + bX2 + *-nXnApplying formula (1) to the case of a spring wheat area we can employ the following definitions:
X= difference between the observed seasonal (May July) precipitation and the mean seasonal (May July) precipitation,, in inches,
X= difference between the mean observed maximum temperature




86
during the season (June July) and the mean maximum seasonal (June July) temperature during a series of year, in degrees Fahrenheit.
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 yields,
b = regression coefficient for mean seasonal maximum temperature on yields,
c = regression coefficient for preseasonal precipitation on yields.
For use in the example, we have assumed the following hypothetical values:
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 increases 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)
Y= 12.3
If a farmer purchases insurance at the 100 percent level he would be entitled, in such a case, to an indemnity equivalent




87
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;_mean~yield.:eould be.,eliminated-froin the
equation by solving directly for the insurance indemnity. From
equation (1) cancel Ya and substitute for Yc 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 appropriate.3 Formula (2), for instance, might be modified as follows:
iSince the insurance carrier bases the premium and indemnity on natural phenomena, price could be removed from the computation. 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 negative.
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 Agricultural Research, LX (1940), 1-23. o 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 involving 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.




88
IM = the modified insurance indemnity,
f = some function of I
and n = some constant of power of I.
Then Im = f(In),
(3) Im = (aX1 + bX2 + nXn) f(In).
For example, if f = 0.1,
and n = 2, then using the data applied to formula (2) we have:
Is = (-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 definite maximum limit would have to be established for Im.
The Premium
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 period.
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 indifferent 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 stability 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




89
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 insurance 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 precipitation, say from August to April, for instance, then the deadline for making the contract would be August 1 of the year prior to harvest. 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 unnecessary, 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
Hor~w 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.




90
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 period 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 appraisal1 of some correlations between yields and the weather factors which are known to influence yields.
Precipitation and Yields
Soil nioisture.--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 important 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.
4Cole and Mathews, op. cit., p. 10.




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TABLE 9
CORRELATION BETWEEN SOIL MOISTURE IN THE SURFACE THREE FEET
OF SOIL AT SEEDING TIME AND YIELD OF WINTER WHEATa
Regression j Correlation
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 Station.
bThe regression equation shows how yields tend to vary with changes in soil moisture at seeding time. We let Y = yield in bushels per acre, and X = percent moisture in the surface 3 feet of the soil at seeding time.
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
(1930), 469-473.
TABLE 10
PROBABILITIES OF OBTAINING SPECIFIED YIELDS OF
WINTER WHEAT WHEN THE SOIL WAS DRY OR WET
TO DESIGNATED DEPTHS AT SEEDING TIMEa
Depth to Failure lO 20 30
Which (4 Bushels Bushels Bushels
Soil b Bushels or or or
was Wetb 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 34Y 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 i0% or 84% or 70% or 23%
aData from measurements taken at experiment station plots at Hays, Colby, and Garden City, Kansas, 1900-1934.
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.
Source: A. L. Hallsted and 0. R. Mathews, Soil Moisture
and Winter Wheat with Suggestions for Abandonment, Kansas Agricultural Experiment Station Bulletin 273 (1936), 41.




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TABLE 11
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 1 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 1 15.9
C and D, Alternately fallowed 6.9 12.6 I 19.9
Avdi~g*c 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.
bIf the second or the third foot contained only 3 percent of available water in course-textured soils or 4 percent in finetextured soils, that soil section was not considered as being wet.
cWeighted.
Source: John S. Cole and 0. R. Mathews, Relation of the Depth to Which the Soil is Wet at Seedin Time to the Yield of SppinpZheat on the Great Plains, U.S.D.A. Circular 583 (May 1940),
10.
It has also been found that a high and significant correlation 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
iRogler and Haas, op. cit., pp. 378-389. Correlation coefficients of .72 and .74 were obtained for the correlation of forage yield and soil moisture in the surface three feet and six feet, respectively. 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.
2Ibid., p. 363. The regressions of forage yield on soil moisture in-the surface three feet and six feet, respectively, were:
Y = 183X + 160, Y = 11IX + 127,
where X = inches of moisture and Y = yield of forage in pounds per acre.