EPA-600/5 74 018
September 1974
Socioeconomic Environmental Studies Series
Crop Insurance and Information Services
to Control Use of Pesticides
4
a)
CD
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and appli-
cation of environmental technology. Elimination of traditional grouping
was consciously planned to foster technology transfer and a maximum inter-
face in related fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL STUDIES
series. This series includes research on environmental management,
economic analysis, ecological impacts, comprehensive planning and fore-
casting and analysis methodologies. Included are tools for determining
varying impacts of alternative policies, analyses of environmental plan-
ning techniques at the regional, state and local levels, and approaches
to measuring environmental quality perceptions, as well as analysis of
ecological and economic impacts of environmental protection measures.
Such topics as urban form, industrial mix, growth policies, control and
organizational structure are discussed in terms of optimal environmental
performance. These interdisciplinary studies and systems analyses are
presented in forms varying from quantitative relational analyses to manage-
ment and policy-oriented reports.
EPA REVIEW NOTICE
This report has been reviewed by the Office of Research and Development,
EPA, and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or commercial products
constitute endorsement or recommendation for use.
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EPA-600/5-74-018
September 1974
CROP INSURANCE AND
INFORMATION SERVICES TO CONTROL
USE OF PESTICIDES
by
John A. Miranowski
UlrichF. W. Ernst
Francis H. Cummings
Contract No. 6 8 -01 -1888
Program Element 1RA030
ROAP 16AFN 03
Project Officer
Marshall Rose, Ph.D.
Washington Environmental Research Center
Environmental Protection Agency
Washington, D.C. 20460
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
For «fde by the Superintendent of Documents, U.S. Government Printing Office. Washington, D.C. 20402 - Price $1.56
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ABSTRACT
This study analyzes the relative effectiveness and efficiency of pest
information and crop insurance programs in encouraging farmers to use
potentially harmful pesticides more sparingly by eliminating wasteful
applications. Possibly excessive applications of pesticides can be at-
tributed to poor timing of applications and to the risk-averse behavior
of farmers. Focusing on insecticide use in cotton production as a major
policy problem, the study employs a decision-theoretic framework to simu-
late the farmer's pesticide use decisions under alternative program
options and subsidy levels. To the extent possible, empirical data are
analyzed to complement the findings of the simulation analysis.
The study framework allows for an internally consistent evaluation of a
set of program alternatives from which the policy maker can select the
most promising option that is feasible within the existing political and
economic context. Since neither the methods nor the data exist to assess
the social costs and benefits of alternative policy options in a reliable
manner, an optimal solution cannot be determined.
The theoretical and empirical analysis in this study indicate that pest
information programs are potentially more effective than crop insurance
programs in reducing insecticide usage. These reductions resulting from
compliance with pest control recommendations provided by information pro-
grams are associated with economic gains by the farmer. Both the simu-
lation experiments and available evaluations of the USDA Pest Management
Program indicate that a maximum insecticide use reduction of 30 percent
can be achieved through information programs. Subsidies to such programs
appear an effective means to encourage adoption by farmers, at least in the
initial phases.
3.1
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CONTENTS
Abstract ii
List of Figures iv
List of Tables v
Acknowledgements vi
Sections
I Conclusions 1
II Recommendations 2
III Introduction 3
IV The Policy Context 11
V Analysis of the Insecticide Use Decision 26
VI Determinants of Program Participation 47
VII Policy Implications 54
VIII References 65
Appendix A—The Mathematical Structure of the
Simulation Model 67
Appendix B—Programming and Sample Run of the
Simulation Model 73
iii
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FIGURES
No. Page
i
1 Schematic Structure of Study Design 9
2 Relationship Between Pesticide Use and Crop Loss/
with Risk Band 27
3 Relationship Between Pesticide Use, Expected Net
Income and Risk 29
4 Probability Distributions of Loss Levels 31
iv
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TABLES
No. Page
1 Total U.S. Cotton Insecticide Usage in 1966 12
2 Insecticide Production Function Estimates 16
3 Expected Losses in Percent and Associated "Risk" 34
4 Expected Net Incomes and Utilities With and Without
Information Programs 40
5 Maximum Expected Utilities for Uninformed Application
Patterns 42
6 Maximum Expected Utilities for Informed Application
Patterns 43
7 Alternative Assessments of Acreage Potential and Cost
for Federal Information Services, Cotton 58
8 Estimated Costs of Expanded Federal Pest Information
Program 60
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ACKNOWLEDGEMENTS
This study has depended on access to unpublished research and unpublished
data. A number of individuals have been critical in providing assistance
in this endeavor. We would like to thank Professors Gerald A. Carlson
and J.R. Bradley, Jr., who served as consultants to the study. They con-
tributed to the development of the methodology and made available data
needed in the investigation. In addition, members of the USDA's Pest
Management Program and cooperating state personnel were very helpful in
providing data and background information on the current pest information
program. Richard Byrness of the Federal Crop Insurance Corporation's
Actuarial Division played a crucial role in obtaining the crop insurance
data used in this investigation. Naturally, none of these individuals
should be blamed for any shortcomings of the study.
What follows constitutes a cooperative effort on the parts of Francis
Cummings, Ulrich Ernst and John Miranowski. Sally Wand showed remarkable
patience in typing and retyping various drafts for this report.
vi
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SECTION I
CONCLUSIONS
Three major policy conclusions emerge from the microeconomic simulation
analysis of farmers' responses to the pest information and crop insurance
policy options examined:
• Pest information programs are potentially effective
in reducing insecticide use in cotton production
without adverse economic effects on the farmer.
The analysis indicates that compliance with pest
control practices recommended by pest information
programs would actually increase expected net in-
comes for the farmer. Both the simulation experi-
ments and the available evidence on the USDA Pest
Management Program suggest a potential reduction
of insecticide use by up to 30%.
• Without information programs, crop insurance programs
appear questionable as instruments to reduce the
social costs of insecticide use. Farmers would
substitute insurance for pesticides, but at a high
cost to society.
• With information programs, crop insurance programs
could reduce insecticide use within reasonable limits.
However, the required subsidies for the relevant in-
surance options would be relatively high.
On the basis of these conclusions, pest information programs appear to be
a more viable policy option. Attracting more (cotton) farmers into in-
formation programs therefore is a reasonable policy objective.
One effective instrument for this purpose is the subsidization of the cost
of pest information services to the farmer. A statistical analysis of the
responsiveness of the demand for pest information services to variations
in the cost of these services to the farmer indicates a fairly high price
elasticity, estimated at slightly less than -2.0. For that elasticity,
a subsidy of the cost of information services of 10 per cent would imply
an increase in participation rates by 20 per cent. Subsidies could there-
fore be used, at least in the initial phases, to establish widespread ac-
ceptance of pest information programs.
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SECTION II
RECOMMENDATIONS
1 i
The results of this study encourage the deliberate expansion of pest
information programs and dissemination of information about potential
program benefits to non-participating farmers and to regions not covered
by existing programs. In addition, the results indicate a need for sub-
sidies to pest information programs, at least in the short term, to
shorten the adoption lag that normally accompanies any innovation or
new production technology. The potential effectiveness and efficiency
of pest information services in reducing excessive pesticide use should
result in a net benefit to society, without creating shortages or higher
prices for farm commodities.
Crop insurance programs appear to be less promising as instruments to
reduce pesticide use in agricultural production. However, further research
is required before this policy option can be disregarded.
Additional research is required in a number of other policy relevant areas.
First, the present investigation focused on one type of pesticide for one
crop, using data from one region. The generalization of the findings to
other crops and regions is therefore somewhat unreliable. Greater relia-
bility could be achieved by applying the methodological framework to other
cases. Secondly, various delivery systems exist for pest information ser-
vices. An economic evaluation of these alternative systems would be neces-
sary to determine the more effective and efficient methods under given
production conditions. Thirdly, the present investigation had to use
data for the average farm. Variations in the scale of farm operations
may affect the results of the analysis significantly. Such variations
should be introduced into the analysis, if the necessary data can be
gathered. Finally, more knowledge is needed on effective means for dis-
seminating new technologies for agricultural production. Although in-
formation program subsidies appear to be effective, other methods may be
more efficient.
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SECTION III
INTRODUCTION
THE POLICY PROBLEM
Chemical pesticides have played an important part in raising productivity
in agriculture by lowering the incidence and severity of crop losses caused
by disease, insects or weeds. However, pesticides currently used may pro-
duce substantial negative side effects in the form of health and reproduc-
tive damage to fish and wildlife, domestic animals and even humans. These
damages constitute real costs to society. Since negative externalities or
social costs of pesticide use fail to influence the farmer's production
decisions, actual pesticide use is likely to exceed the level that would
be chosen if all (private and social) costs were considered.
The present state of the art prohibits a reliable comparison of the social
costs and benefits of alternative pesticide use patterns in agriculture.
The socially most desirable level of pesticide use therefore cannot be de-
termined. Public health considerations suggest a reduction in the use of
chemical pesticides. It is unclear, though, at what point reductions would
lower agricultural productivity sufficiently to create a net loss to
society.
Under these conditions, the public policy option most consistent with
market mechanisms — manipulation of resource prices through taxes and
subsidies to internalize external costs — may result in serious ineffi-
ciencies and distortions. It is therefore necessary to examine alterna-
tive policy approaches to reduce the harmful side effects of chemical
pesticide use in agriculture. The present study focuses on policy op-
tions other than the introduction of less harmful pesticides, such as
natural predators or biologically derived means of pest control. The
identification of such alternatives requires a clear understanding of
the role of pesticides as inputs into agricultural production.
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More than in any other industry, production conditions in agriculture are
subject to elements of chance. Weather conditions, plant diseases and
insect infestations — all crucial in determining actual yield — cannot
be predicted with certainty. Pesticides offer the farmer a way of re-
ducing at least part of the resulting risk. Their use raises expected
yield and lowers the uncertainty associated with actual output.
The effectiveness of pesticides depends on the timing of the application
in response to observed indicators of pest infestation, as well as the
selection of the proper type and dosage of pesticide chemicals. Poor
timing results in wasteful pesticide use. If the farmer lacks the in-
formation or experience to interpret indicators of potential pest damage,
he typically attempts to reduce his risk by periodic or programmed appli-
cations of pesticides. In other words, he is likely to apply pesticides
"mechanically" regardless of the need for these chemicals. This procedure
may actually increase the need for pesticides by destroying the natural
predators of crop pests and increasing pest resistence to the chemicals
used.
One option for the policy maker to curtail such wasteful pesticide use lies
in improving the farmer's understanding of the importance of pest infesta-
tion indicators and of the appropriate pest control response through pest
information programs. Programs currently operating involve two components:
(1) scouting of fields to determine the level of pest infestation, and
(2) disseminating of recommendations concerning the appropriate response to
the observed pest problem.
A second policy option derives from the view that programmed application of
pesticides constitutes a form of "insurance" against the occurrence of crop
pests. Since the (private) cost of pesticides is relatively low, this
approach can be a rational strategy. Thus a potential reduction of pesticide
use could be achieved by providing the farmer with low-cost crop insurance
programs. Subsidized crop insurance is a means of sharing the risk of crop
losses between the farmer and society; it is a viable policy option, par-
ticularly if farmers exhibit risk-averse behavior — which implies "over-
reaction" to perceived pest threats.
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Both information and crop insurance programs are currently in effect.
Their operating experience is fairly limited, though. Their potential
in changing the farmer's choice of pesticide application levels has there-
fore been assessed only in a very rudimentary way. The design of policies
geared toward greater overall efficiency of pesticide use necessitates a
better understanding of the ways in which they can influence the pesticide
use decision process. Such an understanding is the basis for an assess-
ment of their relative strengths. This study presents a framework for this
type of assessment, combining theoretical and empirical analysis. The
nature of the actual analysis is predominantly exploratory; the resulting
policy recommendations are therefore limited to suggestions for potential
policy emphasis and for areas needing additional study.
STUDY DESIGN
The assessment of the relative effectiveness of crop insurance and pest
information programs as policy instruments involves two major issues:
1. How effective are these programs in changing the farmer's
decision parameters and, in turn, pesticide use levels?
2. Under what circumstances would these programs be adopted
by the farmer?
Since participation in either program is voluntary, an important element
in the evaluation of these policy instruments is the conditions under
which they would be adopted. This aspect is addressed by the second issue
The first issue concerns the degree to which insurance or information,
once adopted by the farmer, alters his pesticide use patterns.
The design of the present study is based on the assumption that the under-
standing of the "mechanics" of the pesticide decision process is critical
to resolving both issues. Unless it is clear what the decision parameters
are, it is futile to speculate about the ability of the policy instruments
considered to change these parameters. The first step in the analysis
therefore consists in a conceptual clarification of the decision process
determining the level of pesticide use.
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The conceptual framework employed in this study derives from the interpre-
tation of the role of pesticides as an input into agricultural production
as discussed above. If their function is to reduce the likelihood of
pest damage and to lower the associated risk, the farmer's problem corre-
sponds to the general problem of decision-theoretic research: the choice
of an optimal (pesticide application) strategy under conditions of uncer-
tainty. The central components of the decision-theoretic framework applied
to the pesticide use problem can be summarized as follows:
• For each level of application, the farmer formulates
his expectations concerning the likelihood of dif-
ferent levels of crop loss and the variance of this
crop loss.
• Given the price of the crop, the cost of production,
and the cost of pesticides, loss expectations can be
translated into expectations of net income associated
with alternative application levels.
• Net income expectations and the variance of these expec-
tations form the basis for the determination of ex-
pected utilities associated with each application
level. Expected utilities reflect both the expected
net income and the magnitude of risk.
• The farmer chooses the application level that maxi-
mizes his expected utility.
The analysis in this study uses this structure to develop a formal model
of the farmer's decision process concerning the level of pesticide use.
The formal model is subsequently used in a series of microeconomic simu-
lation experiments of the decision process under alternative assumptions.
The purpose of these experiments is to generate the information required
to resolve the first issue stated above, concerning the impact of changes
in decision parameters on the choice of pesticide application levels.
The experiments are conducted by means of a digital-computer program that
uses numerical estimates of the parameters of loss expectations and
variance of these losses for different application levels and application
strategies, and of other factors involved in the pesticide use decision.
The validity of such a "quasi-empirical" analysis depends on the validity
of empirically relevant parameters and the theoretical specifications
of the model. Parameter estimates have therefore been statistically
derived from available data. This approach necessitates a specific
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empirical focus. While the model itself is sufficiently general to handle
a wide variety of cases, the implementation concentrates on one crop, one
region and one type of pesticide. This restriction is necessary to control
for the influence of different pest problems, pest control alternatives and
crop production environments.
Insecticides were selected as the type of pesticide to be investigated,
since these chemicals have been found to be both the most toxic and the
most persistent. The dangers associated with their use are reflected in
the recent ban on DDT, except for isolated uses, as well as restrictions
on other organochlorine insecticides. Neither herbicides nor fungicides,
the other types of pesticides, raise the same public policy concerns.
Fungicides account for less than 10 per cent of the active pesticide in-
gredients applied; in addition, they have been considered in a previous
decision-theoretic analysis by Carlson [ 3 ].* While herbicides are the
fastest growing pesticide, their usage does not appear amenable to any
significant reduction through subsidized crop insurance or information
services. Weed detection and multiplication problems call for other
solutions, such as mechanical cultivation and crop rotation.
The choice of insecticides as the relevant pesticide category suggests
cotton as the most suitable crop, since insecticide usage is most im-
portant in cotton production. Cotton accounted for 47 per cent (65 million
pounds) of total crop insecticide usage in 1966, the most recent year for
which reliable published data are available [ 8 ]. Unpublished estimates
from the 1971 Farm Expenditure Survey indicate an increase of over ten
per cent in insecticide use on cotton between 1966 and 1971. In addition
to the relatively intensive use of insecticides in cotton production,
there are also significant qualitative reasons for choosing cotton. This
crop uses the largest quantities of organochlorine insecticides, account-
ing for approximately 70 per cent of total organochlorines used in agri-
cultural production. With the current ban on DDT, though, cotton farmers
are substituting methyl parathion (organophosphorus compound) for the or-
ganochlorine compound DDT.
* Figures in brackets refer to the references listed in Section VIII.
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Concentration on a single region is justified by the greater sensitivity
of the results to actual production conditions. Parameters estimated on
a national basis could introduce considerable "noise" into the analysis
by concealing significant differences among regions. For the present
study, the South has been chosen, including the Mississippi Delta, the
Southeast, and parts of Appalachia. This area accounts for slightly less
than half of the total 1972 cotton output, according to data released by
the Department of Agriculture [ 22 ]. In addition, insecticide usage in
cotton production is higher in this region than in others.
t
The choice of cotton as the focal crop provides a comparatively favorable
data base for the analysis of the first issue, the potential of pest
management information and crop insurance programs to "reach" the farmer.
Cotton has already been subjected to extensive analysis with respect to
the insecticide problem. Although research efforts have focused on the
impact of bans on specific insecticides on production costs and yields,*
the information gathered in previous studies establishes an empirical
background for the present investigation. In addition, cotton producers
have participated in scouting and pest management information programs
for a number of years. While these programs have been isolated and limited
in scope, some data have been collected, program structures have been
established, and rudimentary evaluation studies have been conducted. These
data are essential for going beyond the assessment of the potential impact
of the policy options studied here under idealized conditions. For
example, data from the Federal Crop Insurance Corporation can be used to
assess subscription patterns on an empirical basis.
The results of the simulation experiments and the findings of the empirical
analysis concerning the ability of information and insurance programs to
secure participation by farmers .are subsequently combined to formulate
policy recommendations of a more general nature. The design structure of
this study is presented in graphical form in Figure 1.
* Examples for these studies are Cooke [ 4 ], Cooke, Berry, and Fox [ 5 ] ,
Texas ASM University [ 19 ], and Pimentel and Shoemaker [ 16 ]; for an
evaluation of alternative approaches to change insecticide use, not spe-
cific to cotton, see Dixon, Dixon, and Miranowski [ 7 ] .
8
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Review of
Existing
Programs
Analysis of
Role of In-
secticides
in Cotton
Production
Analysis of
Determinants
of Farmer
P arti cip ation
in Programs
Simulation
Analysis of
Insecticide
Use Decision
For Alterna-
tive Policies
Assessment
of Potential
of Alterna-
tive Policy
Options
Analysis
of Policy
Impli cations
Figure 1. Schematic Structure of Study Design
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STRUCTURE OF THE REPORT
The structure of the presentation in this report reflects the overall de-
sign of the study. The first step is the establishment of the context
within which pest information and crop insurance programs in cotton pro-
duction. Section IV presents an overview over the role of insecticides
in cotton production and reviews the experience of public programs current-
ly in operation* This review establishes the basis for the development of
the decision-theoretic analysis, presented in Section V.
The discussion of the results of the simulation analysis, indicating the
potential impact of pest information and crop insurance programs, is fol-
lowed by an assessment of the factor influencing the participation of
farmers in these programs. Section VI presents empirical evidence on the
sensitivity of participation patterns to variations in the cost of parti-
cipation to the farmer. The policy implications of the findings of this
study are examined in Section VII.
10
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SECTION IV
THE POLICY CONTEXT
INTRODUCTION
This section presents an overview of pest management problems in cotton
production and describes current policy programs in pest information and
crop insurance. This review establishes the macro-analytical framework
for the microeconomic investigations described in subsequent sections.
The first section focuses on the extent of insecticide use in cotton pro-
duction and examines the role of these chemicals as productive inputs.
This analysis includes the specification of empirical production functions
for insecticides. The next section reviews the characteristics of pest
management information programs currently operating and presents the
available evidence as to the effect of these programs on insecticide use
patterns. This discussion is followed by an overview of the major public
crop insurance program offered through the Federal Crop Insurance Corpo-
ration.
INSECTICIDES IN COTTON PRODUCTION
It is difficult to estimate current insecticide use in agricultural pro-
duction. Reliable data are available only for 1966, before the ban on
DDT. These data were compiled by Eichers for the Economic Research
Service of the Department of Agriculture [ 8 ]. Table 1 shows the amounts
of different types of insecticides used in cotton production for 1966.
The second column shows estimated usage pattern under the assumption of
a ban on DDT. These estimates can be used as approximations of current
insecticide use. Although acreage changes have occurred , quantities of
insecticides used on cotton have not changed significantly.* However,.
unpublished estimates from the 1971 Farm Expenditure Survey indicate some
Source: Conversation with Dr. Austin Fox, Head, Pesticide Research Group,
ERS, USDA.
11
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Table 1. TOTAL U.S. COTTON INSECTICIDE USAGE IN 1966
(In 1,000 Pounds of Active Ingredients)
Type of Insecticide
Organochlorines
Lindane
Strobane
DDT
Endrin
Aldrin
TDE
Toxaphene
Others
Organophosphorus
Disulfoton
Bidrin
Methyl Parathion
Malathion
Trichlorfon
Azinphosmethyl
Others
Actual
Usage
163
2,016
19,213
510
123
167
27,345
166
300
2,857
2,181
559
963
200
285
Estimated , a
Assumed Ban on
DDT
163
2,016
0
510
123
0
49,228
166
300
2,883
2,181
559
1,447
442
285
a Insecticide usage under a DDT ban was estimated on the basis of the
following assumptions: 1.2 treatments of toxaphene-methyl parathion
would be needed to replace the former toxaphene-DDT-'-methyl parathion
combination; new application rates would be 50% higher for toxaphene
and six times greater for methyl parathion. Other minor changes were
needed in bidrin, trichlorfon and azinphosmethyl to adjust for situa-
tions in which DDT was used alone.
Sources: Eichers et al. [81, Davis et al. [6 ] , and Cook6 [ 4 ].
12
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increase in the total quantities applied.
The intensity of insecticide use in cotton production is relatively high
compared to other crops; it is surpassed only by apple growing. Usage in
1966 amounted to approximately 6.3 pounds per acre of cotton cultivated;
the amount per acre appears to have slightly decreased by 1971. There are
significant interregional variations in the intensity of insecticide use:
for 1966, the quantity of active insecticide ingredients applied per acre
per year averaged approximately 9 pounds in the Mississippi Delta, over
15 pounds in the Southeast, and morfe than 5 pounds in the Appalachian
states. All other cotton-producing regions averaged less than 5 pounds.
These averages abstract of course from substantial variations among sub-
regions and among individual cotton producers.
These data provide an impression of the magnitude of the insecticide use
problem in cotton production. A more differentiated assessment of the
importance of insecticides requires an understanding of their function in
reducing the likelihood and severity of insect damage to the cotton crop.
It is difficult to develop such an understanding on the basis of "real-
world" data, since insecticides constitute only one input among many.
Their effectiveness depends on the application "technology," cultivation
methods, infestation levels/ and weather conditions. This interaction
with other factors partially under the control of the agricultural pro-
ducer necessitates a large data base for determining the impact of in-
secticides empirically. Such a data base does not exist in the form re-
quired.
Fortunately, the analysis of the relationships between agricultural inputs
and outputs can draw on data obtained under experimental conditions in
agricultural research stations. For the present purpose, a review of
available data relating crop yields to different levels of insecticide
application indicated that the most appropriate data described the results
of experiments conducted during 1962-1964 at the Wiregrass Substation in
Alabama, as provided by Watson and Sonyers [24]. These experiments were designed
to test various insecticide treatment schedules. They included variations
13
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of application patterns. Two experimental alternatives have been se-
lected for the analysis here, since they describe two extremes in applica-
tion procedures. The "complete season control" alternative consisted of
automatic sprayings at prespecified intervals, yielding between 24 and
26 applications per season. This application pattern can be viewed as
typical for the farmer who lacks the information or experience to inter-
pret indicators of impending pest damage, and who attempts to minimize
risk by using pesticides "blindly," regardless of need. The second ex-
perimental alternative selected for the analysis presents a more dif-
ferentiated approach: insecticides were sprayed only when scouting in-
formation showed current infestation levels exceeding a 25 per cent
threshold. This alternative can be interpreted as representative of a
farmer who makes maximum use of available information. These two data
sets have been used in this study to derive statistical estimates of the
relationship between amounts of insecticides used and the associated crop
yield. This relationship is akin to a (one-factor) production function.
The statistical analysis requires the prior specification of a functional
form of the relationship. This specification should reflect assumptions
about the marginal productivity of insecticides; if other inputs are held
constant, it is reasonable to expect declining marginal productivities.
This assumption precludes the use of a linear functional form, since such
a production function would imply constant marginal productivities. This
elimination leaves the quadratic and multiplicative (Cobb-Douglas) forms
as alternatives. The multiplicative form, which allows for declining
marginal productivities, creates a serious estimation problem, once zero
input levels are allowed.* Because of these shortcomings of the two major
alternatives, the quadratic form of the production function has been used
in the empirical analysis. It allows for declining marginal productivities
of insecticide use without raising estimation problems. This form has
been applied to the analysis of the results of experiments conducted by
agricultural research stations with some success, e.g. by Heady and
Tweeten [ 12 ] and Heady and Dillon [ 11 ]. Other investigators, such as
* Zero input levels prohibit the logarithmic transformation required for
linear-regression analysis; the addition of a constant to all observa-
tions may introduce biases into the resulting estimates.
14
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Sutherland, Carlson and Hoover [ 18 ] and Huffman [ 14 ] , have used the
quadratic production function successfully in the analysis of actual farm
survey data.
These considerations delineate the insecticide production function tested
as follows:
Y = b + b. X + b0 X2 + u (1)
O 1 2
where Y = cotton yield, pounds of cotton lint per acre;
X = insecticides, pounds applied per acre;
b. = regression coefficients (i = 0, 1, 2);
u = disturbance term.
The assumption of declining marginal productivities implies that b , the
coefficient of the squared term, is negative.
The regression parameters for the two data sets were estimated by ordi-
nary least squares. The results are shown in Table 2 for the two alter-
native application patterns, "complete season control" and for 25% in-
festation levels only. In both cases, the regression coefficients b and
b are significantly different from zero; in addition, they exhibit the
expected signs. The regression equations also provide satisfactory ex-
planations of the behavior of the dependent variable, as indicated by the
multiple correlation coefficients which are significantly different from
zero (at the 95% confidence level).
If the marginal physical product of insecticides implied in the regression
equations displayed is used as a measure of overall efficiency of the two
application methods, switching from "mechanical" application to spraying
in response to need would imply a 10% increase in production efficiency
at the average application level of 6.3 pounds per acre. This figure is
of course illustrative only; the decision-theoretic analysis in Section V
uses the evidence presented here and subjects it to a more formal assess-
ment of the implications of alternative insecticide use patterns.
15
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Table 2. INSECTICIDE PRODUCTION FUNCTION ESTIMATES
Regression Programmed (Periodic) Application As Needed
Coefficients Application (25% Infestation)
b 516.75 574.61
b 21.80 24.13
(5.53) (5.43)
b2 -.23 -.32
(-4.61) (-4.58)
R2 .804 .653
Sample Size 12 21
t-Statistics in parentheses.
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This brief analysis of the role of insecticides in cotton production
establishes the background for a review of the experience of existing
pest information and crop insurance programs. Such a review is neces-
sary to direct the analysis of the pesticide decision. In addition, it
provides the background for the analysis of the feasibility of desired
changes in institutional and financial arrangements.
PEST INFORMATION SERVICES
Pest management information services can assist the cotton farmer in three
ways: first, by providing him with accurate and up-to-date data on the
level of pest infestation in his fields; secondly, by making recommenda-
tions for insecticide applications on the basis of field data; and thirdly,
by providing suggestions improved techniques of pest management. Infesta-
tion data are gathered through scouting efforts, in which workers trained
in the recognition of harmful and beneficial insects, as well as diseases
and other important crop conditions, are paid to check fields once or
twice a week.
Insecticide application recommendations are based on the rationale that
insect control measures are necessary only when infestation in a parti-
cular field reaches an economic threshold level. This concept is defined
as the infestation level at which the economic cost of reduced crop sales
is predicted to exceed the cost of applying corrective pesticides or
taking some other pest control measure.* The application of this concept
to pest management requires data on actual infestation levels, as well as
the expected yield reduction caused by different levels of infestation
under given cultivation methods and weather conditions. In addition, the
prediction of monetary losses requires assumptions about the future market
price of the crop. The estimation of the total cost of corrective action
must account for direct costs of application, as well as the indirect
effects through disturbances of the ecological balance between harmful
insects and their natural predators.
* Another, less rigorous definition is also widely used; it sets the
threshold at that level of infestation that is expected to cause
any reduction in crop yields.
17
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Scouting programs are a crucial input into integrated pest management
systems. Such systems employ a combination of pest control techniques,
ranging from utilization of natural controls to a variety of counter-
measure by the farmer. Because of the extreme complexity of such a com-
prehensive approach to effective pest control, it demands reliable data.
In addition, integrated pest management by the farmer necessitates assis-
tance in interpreting scouted field data and in the selection of the most
appropriate control techniques. By establishing an on-going relationship
with farmers, scouting programs are able to fulfill this assistance role.
The rapid development of private and public sector pest information ser-
vices is the result of a combination of increasing environmental concerns,
the growing difficulties of pest control through chemical insecticides,
and a growing body of research indicating that insecticide applications can
be reduced substantially with little or no adverse effects on yields.
By 1972, about one-fourth of the U.S. acreage planted to cotton was scouted,
or about 3.4 million acres [ 20 ]. The largest share of this acreaged, 1.3
million acres, is scouted by private-sector entomological or general agri-
cultural consultants. Extension trained scouts cover approximately 866,000
acres of cotton through the USDA-sponsored Pest Management Program and
various state scouting programs. Growers themselves, or their employees,
scout an additional 791,000 acres. The remainder of the acreage covered
is scouted by the local sales representatives of the chemical industry
(332,000 acres) and cotton gins and cooperatives (105,000 acres).
The USDA Pest Management Program
During its first year of full-scale operation in 1972, the USDA Pest
Management Program provided Federal funds to 22 programs in selected
counties in several states to establish new or subsidize existing field
scouting operations, to develop computer data management systems for in-
formation on pest populations and other aspects of farm conditions and
operations, and to make recommendations to growers about pest management
practices. This program can be regarded as a model for a Federally-spon-
sored information service.
18
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Over the period 1972 through 1974, the Cotton Pest Management Program re-
ceived a total of $650,000; these funds financed operations in fourteen
states. In 1972, the Cotton Pest Management Program covered almost 5,000
producers with 574,000 cotton acres in 111 counties. Participating pro-
ducers averaged 125 acres of cotton, which is high compared with the U.S.
average of 70 acres per cotton farmer. The Program employed 484 scouts
with an average workload of roughly 1,200 acres each. On the average,
one scout supervisor was responsible for every twelve scouts. These
figures are of course only average; Program characteristics varied sub-
stantially among cotton producing regions and states.
Available data indicate a total cost per acre scouted of $2.99 for 1972
and $3.18 for 1973. The following breakdown describes the sources of
funds:
1972 1973
PMP Grant Funds .82 1.13
Producer Payments 1.40 1.36
Extension Contributions .70 .63
Other .07 .06
Total Cost per Acre $2.99 $3.18
The 1973 Pest Management Program contribution of $1.13 per acre in grant
funds to the scouting programs constitutes a 36% subsidy of the total
cost of $3.18; if other direct and indirect subsidies are included, this
percentage increases to 57%.
Our survey of persons responsible for Cotton Pest Management Programs in
most cotton-producing states indicates that the total per acre varies from
$2.00 to $5.00, depending on the services provided, and — to some extent
— on regional characteristics such as the length of the growing season.
Costs can run higher for private-sector programs which essentially assume
decision-making responsibility for a grower's pest control program.
19
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Private Scouting Services
Private entomological consulting firms have been active in scouting and
formulating recommendations for pest management for a number of years.
The first private sector scouting services available were operated by
chemical companies and distributors. More recently, entomological con-
sultants and consulting firms have begun to offer producers a wide range
of pest management services, including scouting and recommendations based
on infestation data.
In some states, the USDA Pest Management Program has relied heavily on
these private firms. For example, the California program contracts out
its scouting with Federal funds. In many other states, the USDA Pest
Management Programs see their role as initiating scouting programs only
in areas where private scouting services have not covered most of the
acreage. This need varies among regions. In Mississippi, for example
a single company (Agriculture Consultants) scouts more than half of the
state cotton acreage.
This important role of private scouting services suggests that the need
for Federally-sponsored programs may be limited. It is conceivable to
view such programs as "seed efforts," operating only for a limited time
in areas not participating in scouting programs as yet — until producers
have realized the potential of these services and are willing to purchase
pest management information services on their own and to comply with
recommendations based on the economic threshold concept.
Evaluations of Existing Pest Information Programs
Most of the state-level Cotton Pest Management Programs have undertaken
or sponsored evaluations of the effectiveness of the services provided
to farmers in reducing pesticide use and in improving farm incomes [ 23 ].
A survey in Alabama showed that participants in the scouting program made
two less applications of pesticides in 1972 than in 1971, for a saving of
$4.00 per acre, corresponding to an average of nearly $500 per farmer.
Two applications less represent a reduction in pesticide use of about 13
20
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per cent, given an average of 14 to 16 applications per year for the state.
Data for other states are comparable; Arkansas reported an average reduc-
tion of insecticide use by four applications per year, Mississippi almost
three, and Louisiana two to three. Generally, these reports did not con-
tain data on the associated impact on cotton yields realized by partici-
pants. It is therefore impossible to assess the net benefit (cost) to the
cotton farmer.
A more detailed evaluation of their program has been prepared by Arizona
program personnel, entitled "An Evaluation of Pesticide Use Practices by
Final County Cotton Pest Management Program Participants in 1972." The
data summary presents no data on cotton yield, but it does contain de-
tailed data on the effectiveness of pest information services. Three
principal findings are of interest here:
1. About 50% of the cotton acreage covered by the scouting
program was sprayed according to need, that is, in com-
pliance with recommendations based on scouted field in-
festation information. The other 50% was sprayed ac-
to automatic schedules or other previously established
patterns.
2. The acreage sprayed according to need was treated with
insecticides about 30% fewer times per acre per year
than the rest of the acreage in the program. This is
the amount of pesticide reduction that could have been
achieved by all participating farmers if all of them
had followed the program recommendations based on^
scouted field information.* \
3. The total acreage covered by the scouting program was
treated 16% fewer times than the portion of the acre-
age sprayed according to previously established patterns.
It falls short of the maximum of 30%, since only half of
the participating acreage was sprayed according to re-
commendations .
Although the variation between large and small farms in Pinal County,
Arizona was significant, the reduction in pesticide usage was substantial
for all farm sizes. The data reported show a clear trend for larger
farms to devote a smaller share of their acreage to treatment based on
need than smaller farms. In addition, larger farmers who follow program
* It is interesting to note that this percentage reduction corresponds
almost exactly to the percentage reduction resulting from the intro-
duction of information program recommendations in the simulation ana-
lysis discussed in Section V.
21
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recommendations tend to achieve less reduction in the number of applica-
tions than smaller farmers.
It is difficult to interpret or generalize these findings adequately,
partially because of the small sample size (54 growers with about 18,000
acres) . and its limitation to one state. The analysis also assumes that
the number of applications can be viewed as a satisfactory approximation
of the amount of insecticides applied, and that growers participating in
the information program who failed to follow program recommendations are
typical for farmers who lack scouting information. These assumptions
may be somewhat simplistic. Furthermore, it is possible that reductions
in pesticide use should be attributed to factors other than participation
in scouting programs. Even so, the evaluation of the Arizona experience
suggests the dimensions of the potential of pest information services.
Ganyard and Worley [ 9 ] have examined the impact of pest information
programs on farm profits. They analyzed the yields and the costs of in-
sect control among farmers participating in the Cotton Pest Management
pilot projects in North Carolina. Their results indicate that partici-
pants in the projects, which coordinate scouting programs, the purchase
of chemicals, and the arrangements for aerial applications, obtained
substantially higher yields with only slightly higher insect control
costs than producers who did not participate. The specific contribution
of the scouting and information component to the greater profitability
among participants could not be quantitatively isolated, but the authors
believed that this component had a highly positive effect.
Summary
The available evidence on the impact of pest information services on in-
secticide usage patterns is sketchy. It. does not allow for a clear de-
termination of the implications of participation in such a program on
farm income. However, it appears that compliance with pest information
program recommendations may reduce insecticide usage by as much as 30
per cent. This reduction does not appear to entail reductions in farm
income.
22
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CURRENT CROP INSURANCE PROGRAMS
One of the premises of this study states that pesticide use in agricultural
production is a means by which the farmer reduces his risk. An alternative
method consists in purchasing risk coverage in the form of an insurance
policy. It is possible that a sharing of the risk associated with agri-
cultural production between the farmer and the public sector through some
form of crop insurance would result in a reduction of pesticide applica-
tion levels. The following discussion provides a brief overview of crop
insurance programs currently available to the farmer.
Federal Crop Insurance
Federally sponsored crop insurance is made available to farmers by the
Federal Crop Insurance Corporation (FCIC). This insurance program covers
all risks of crop loss encountered by the farmer, but the FCIC program is
not intended to compensate farmers for the full crop value lost. Federal
crop insurance coverage is limited to production expenses, which cannot
exceed 75 percent of county average yield. Although production expenses
as a share of average yield vary from county to county, they typically
constitute roughly 60 percent of county average yield. Thus, FCIC cov-
erage is limited to losses exceeding 40 percent of average yield in the
county; essentially a 40 percent deductible provision for the average
cotton farmer.
The FCIC program is also restrictive in the determination of indemnity
payments. If the actual yield for a particular crop on the entire farm
falls below the county average yield at harvest time, the farmer re-
ceives an indemnity payment based on the difference between actual and
(county) average yield. The dollar value of coverage is determined
by the price option the producer selects when he purchases the insurance
coverage. The actual indemnity payment is the product of the price option,
the difference between actual and county average yield (expressed on a per
acre basis), and the number of cotton acres on the farm.
*A11 fields of the particular crop on a farm must be insured if the farmer
wants to participate in the FCIC program. The average yield used to de-
termine losses is computed across all fields used in growing the particu-
lar crop on the participating farm.
23
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Premium levels are determined by actuarial statistics for the given crop
in the particular county. These levels vary with the price option selected
by the producer, who can choose one of three price options — rather
abritrarily established by the PCIC -- to determine the dollar value of
his insurance coverage.
The FCIC program is less flexible than specific-risk insurance programs
offered by the private insurers, although it provides coverage for a wider
variety of risks^ The structural provisions of the FCIC insurance program
reduce its potential as an effective means of reducing cotton production
losses due specifically to insect damage. As noted above, FCIC cotton
coverage is limited to losses exceeding approximately 40 percent of county
average cotton yields. At the same time, the maximum loss from insect
damage in cotton production seldom exceeds 40 percent of cotton yields.
With the equivalent of a 40 percent deductible, FCIC coverage for losses
due to insect damage alone would seldom become effective, if at all. Al-
though some variation in yield guarantee within a county is possible and
other risks are covered, there is little incentive to purchase current
all-risk crop insurance to cover the losses from insect damage.
Another provision makes the FCIC insurance program a doubtful policy in-
strument for reducing insecticide use. Program participants are required
to employ "good production practices," including accepted insect control
measures. Under the present legislative structure of the FCIC program,
participating producers do not have the option of using insurance as a
substitute for "necessary insecticide treatment"; such a substitution could
only be made for "excessive treatments" resulting from a programmed insec-
ticide application procedure.
Private Crop Insurance
Private insurance companies offer specific-risk crop insurance to farmers,
primarily against hail damage. This type of insurance can be purchased
with yield and price coverage up to the full value of the expected crop.
Indemnities are generally based on the portion of the growing crop lost
to hail; the percentage of the crop lost is determined immediately after
24
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occurrence of the damage by an adjuster. Under specific-risk insurance,
indemnities are calculated on the basis of the loss percentage times the
coverage for individual acres damaged by a specific threat. Private in-
surance options differ from the FCIC provisions in two other respects:
coverage can be purchased for part of the crop, and it can be purchased
at any time as opposed to planting time for FCIC coverage.
Specific-risk insurance could be extended to cover insect damage to the
crop. The provisions of such an insurance scheme could be analogous to
the hail insurance framework currently offered by private insurance com-
panies. The program could be operated either by the public sector or
by private companies, possibly with appropriate subsidies to reduce the
premium cost to the farmer. Variations in the pest control requirements
for subscribers (such as participation in an integrated pest management
program) could be integrated into the insurance provisions. Although
these variations are of interest to the policy maker, the theoretical
analysis in Section V focuses on simpler insurance schemes.
SUMMARY
The discussion in this section provides an overview over the current
context of the insecticide problem in cotton production. The available
evidence indicates that insecticides are an important input into the
production process for the cotton crop. Pest information exhibit some
potential to improve the efficiency of insecticide usage, leading to
a reduction in application levels without lowering farm incomes. Public
crop insurance programs currently are limited to the all-risk FCIC
scheme which shows some deficiencies as an instrument for reducing
insecticide usage. Specific-risk insurance, similar to insurance against
hail damage currently offered by private insurance companies, appears to
offer greater flexibility.
25
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SECTION V
ANALYSIS OP THE INSECTICIDE USE DECISION
THE CONCEPTUAL FRAMEWORK
The analysis of the role of insecticides as inputs into cotton production
in Section IV establishes the basis for the conceptual framework for the
decision-theoretic analysis here. The production functions describe the
expected yield for any given amount of insecticides; viewed from a dif-
ferent angle, they specify the expected loss relative to some maximum
yield. The actual loss for a given amount of insecticide varies in re-
sponse to other factors, but is likely to fall within a definable range.
Given the shape of the production functions estimated in Section IV, the
expected loss decreases with increasing amounts of insecticides at least
up to a point. It is reasonable to assume that the range (variance) of
percentage losses also decreases with increasing application levels.
This relationship is illustrated in Figure 2. In this schematic presen-
tation, the average loss for each level of insecticide use is indicated
by the solid lines, while the likely range of percentage losses is sketched
by the shaded bands.
For the farmer's decision concerning insecticide use, this relationship
is not immediately relevant. The farmer is concerned about (net) income
levels, rather than the physical crop yield. If the relationship between
monetary income and physical yield were linear, the solution to the de-
cision problem would be obvious: since lower losses are always preferable
to higher ones, and smaller preferable to greater risks, the fanner would
apply that amount of insecticides for which the production function attains
a maximum. However, the relationship between net incomes and percentage
crop losses is non-linear. This feature may raise the need for evaluating
tradeoffs between expected loss and risk.
In simplified terms, the necessity of a tradeoff between expected monetary
income and risk may occur as a result of increases in the cost of production
caused by higher expenditures on insecticides. The farmer's net income is
26
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Percentage
Crop Loss
Level of
Pesticide Use
Figure 2. Relationship Between Pesticide Use and
Crop Loss, with Risk Band
27
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defined as total revenue less cost of production. The cost of production
can be broken down into "fixed costs" and the costs of insecticides.
Under conditions of price maintenance programs, as in the case of cotton,
total revenue is directly proportional to actual physical crop yield.
Since actual crop yield can be expressed as maximum yield less pest losses,
total revenue becomes a direct function of the percentage crop loss. The
percentage crop loss is assumed to be a function of the amount of insecti-
cides applied. If the cost of production (other than insecticide costs)
remain constant for different loss levels, the expected net income becomes
a function of two factors that depend on the amount of insecticides used:
expected crop loss and insecticide costs.
The level of insecticide use also affects the variance of net income ex-
pectations, or the monetary risk. This risk factor declines consistently
with increasing amounts of insecticides. The expected net income, however,
is likely to increase initially in response to lower crop losses; there is
a point, though, at which the increasing costs of greater amounts of in-
secticides will outweigh the gains from reduced losses. These relation-
ships are illustrated schematically in Figure 3. In this illustration,
the expected net income reaches a maximum for the insecticide application
level OA. To the right of A, the achievement of lower risk must be "paid
for" by a reduction of expected net income. From that point on, the se-
lection of a particular level of insecticide use depends on the relative
weights that the farmer attaches to his two decision criteria, expected
net income and risk.
This simple framework facilitates the understanding of the basic nature of
the problem. However, it is inadequate for studying more complex situa-
tions. A decision-theoretic approach allows for a more rigorous analysis.*
Two elements are important in such an approach. First, the rather loose
concepts of expected loss and risk are replaced by subjective expectations
of the likelihood of different loss levels for a given level of insecti-
cide application. For each level of insecticide use, these subjective
expectations can be described in terms of a probability density function
* Perhaps the most useful reference work on decision-theoretic research —
with a number of examples from agriculture — is Halter and Dean [ 10 ].
28
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Risk,
Net
Income
Expected
Net Income
Risk
Level of
Pesticide Use
Figure 3. Relationship Between Pesticide Use/ Expected
Net Income and Risk
29
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that specifies the conditional probabilities the fanner assigns to dif-
ferent loss levels, given a particular level of insecticide use. For
example, if all losses within the "risk band" are equally likely, the
farmer's loss expectations could be described by a uniform distribution.
It is reasonable to assume, though, that the likelihood of losses is
clustered around the expected values, and that higher loss levels have
lower probabilities. These assumptions can be sketched in graphical form
in a three-dimensional version of Figure 2, as shown in Figure 4.
The second important element in the decision-theoretic approach is a
utility function that assigns a single value to any given combination
of expected net incomes and risk. Generally, the utility measure is
directly related to expected net income; if the decision maker (farmer)
is risk-averse, utility is inversely related to risk. Thus, the utility
function describes in quantitative form the tradeoffs the farmer is
willing to make between expected net income and risk.
ANALYSIS APPROACH
The decision-theoretic framework for the analysis of the insecticide use
problem forms the basis for a microeconomic model used in this study to
simulate the farmer's decision process. This model incorporates the
following elements:
• the possible actions of the farmer are described in
terms of different amounts of insecticides applied
on a per-acre basis in 5-pound increments;
• for each insecticide amount, the farmer's loss ex-
pectations are described in functional form on the
basis of empirically derived parameters for the
relationships sketched in Figures 2 and 4;
• for each insecticide amount, there exists a unique
functional relationship between crop losses (per-
centage of maximum possible yield lost to pests)
and net income; this relationship expresses net
income as total possible income minus the value of
the crop lost and the cost of pesticides;
• associated with each income/risk combination is
a utility measure that reflects the farmer's pre-
ferences between expected income gains and increases
in risk.
30
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•a
0)
Crop Loss in Per Cent
Figure 4. Probability Distributions of Loss Levels
31
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These components outline the structure of the simulation model.* The de-
cision rule used in the actual simulation states simply that the farmer
selects the action (applies the amount of pesticides per acre) that maxi-
mizes his expected utility.
The model was subsequently translated into a computer program to perform
the required computations. This procedure requires quantitative esti-
mates of the parameters of loss expectation functions for different
levels of insecticide use, and the specification of the net income and
utility functions. In addition, the simulation experiments necessitated
the specification of "prototypical" policy options for Federally subsi-
dized crop insurance. In the case of information programs, data limita-
tions constrain the analysis to two extreme cases, as discussed in greater
detail below.
PARAMETER SPECIFICATIONS
The most important input into the simulation of the farmer's decision
process are the parameters of the (conditional) loss expectation functions
for alternative levels of insecticide use. Carlson [ 3 ] has developed
a survey approach to obtain estimates of loss expectations for crop di-
seases in peach production. This approach could not be used in the pre-
sent study, primarily because of resource constraints. A suitable alter-
native is the use of the production functions presented in Section IV.
The use of these functions in deriving expected losses is relatively
straightforward. The first step consists in determining the maximum
possible crop yield for each of the two application patterns. The
second step uses five-pound increments of insecticides (from 0 to 40
pounds) to compute expected yield for any of the nine actions considered
in the model. The comparison of expected yield for each level of insecti-
cide use with the maximum possible output yields the percentage of crop
lost to pests. These estimates are reported in Table 3.
* The mathematical structure of the model is discussed in greater detail
in Appendix A.
+ Appendix B presents the flowchart of the FORTRAN IV program used as well
as a printout of a sample run.
32
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Table 3. EXPECTED PERCENTAGE LOSS ASSOCIATED "RISK"
(STANDARD DEVIATION), AND RELATED PROBABILITIES
AREAS WITHIN RISK BAND FOR GAMMA-FUNCTION
u
OJ
Pounds of
Insecticides
Per Acre
0
5
10
15
20
25
30
35
40
Uninformed
Expected
Loss (y)a
50
40
32
24
17
12
7
4
2
Application Patterns
"Risk" (a)b
-50
49
46
43
38
32
25
19
14
Risk Band
c
Probability
.865
.872
.881
.893
.906
.920
.939
.956
.972
Informed
Expected
LOSS (y)a
38
27
18
11
6
2
.4
.4
2
Application
"Risk" (CT)b
48
44
38
31
24
14
6
6
14
Patterns
Risk Band
Probability
.875
.888
.904
.923
.944
.972
.991
.991
.972
The expected percentage of crop loss to insects at alternative insecticide application levels.
"Risk" is represented by the standard deviation (percentage units) of the expected crop loss at alternative
insecticide application levels and is based upon the variance formula for a Bernoulli trial.
CProbability that the actual loss falls in the interval (ii-a,u+a ), given a gamma-type probability density
function (with unadjusted probabilities).
-------
The determination of the loss variance (risk) for each level of insecticide
application raises a number of problems. One possibility is the use of the
confidence bands around the regression line as measures of risk. However,
this possibility has the disadvantage that the estimate of risk would become
sensitive to the sample size used in the specification of the regression
equation. For example, the procedure would yield higher risk factors for the
"as-needed_ application pattern than for the programmed application, which
does not appear intuitively acceptable.
Because of these problems, an alternative procedure has been used in specify-
ing the risk factors for each level of insecticide use. For each quantity
of insecticides applied, the expected percentage loss can be interpreted as
the probability of losing one unit of the crop because of the occurance of
pests. In other words, the expected percentage loss for each unit of the
crop represents the "success probability" p on a Bernoulli trial which has
two possible outcomes — pest damage (loss) or no damage. The variance of
the expected percentage loss for a particular action is given by j?(l-p), and
this parameter represents the risk factor for each action. The results of
these calculations for the two application patterns/plus the probability that
the actual loss falls in a given confidence interval, are shown in Table 3.
The basic structure of the relationship between percentage crop loss and net
income has already been discussed above. For the actual simulation, these
assumptions were summarized in the net income function:
y = py (1-s) Y* - TC - p^X, (2)
where y = net income per acre,
p = fraction of crop lost due to insect damage,
y a function of the amount of insecticides applied;
y* = maximum possible crop yield per acre;
TC = cost of production per acre, assumed to be constant;
p = price per pound of insecticides used;
A
X = amount of insecticides used, in pounds per acre.
This specification of the net income level as a function of loss identi-
fies the remaining parameters to be estimated for the simulation model.
34
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The price per pound of cotton lint has been set at $0.40, which corresponds
to recent price levels in the cotton market. For determining the maximum
possible yield of cotton lint per acre, the data from the agricultural
research used in estimating the insecticide production functions were com-
pared to actual production data published by the Department of Agriculture
[ 22 ]. The maximum derived from the regression equations appeared too
high for a realistic simulation. Based on USDA data, the maximum yield
per acre was therefore estimated at 700 pounds of cotton lint. The
"fixed cost" of production also has been estimated on the basis of USDA
data; the figure used is $170.00 per acre.
One of the most difficult parameters is the price per pound of insecti-
cide. Given the wide variety of possible insecticide combinations, cor-
responding to different treatment mechanisms, prices per pound of "average"
insecticide are only crude approximations. For the simulation, this para-
meter has been established at $1.70 per pound of active ingredients. This
estimate is based on the assumption that the average price per pound of
insecticides used in the study region amounts to $1.50, and that the cost
of application per pound per acre is $0.20. These estimates were derived
from a number of sources, primarily USDA data.
The utility function, finally, has been specified consistent with the as-
sumption of risk aversion as a behavioral characteristic of farmers. As
long as this assumption is satisfied, the specific functional form does
not alter the results significantly. The form finally used is the loga-
rithmic one.*
SPECIFICATION OF POLICY OPTIONS
The simulation experiments focused on the effects of pest management in-
formation and crop insurance programs on the decision parameters of the
farmer and the resulting variations in insecticide use. For- greater re-
liability of the results of the simulation analysis, it is desirable to
examine a number of policy options.
* For a more detailed discussion of the characteristics of the utility
function, see Appendix A.
35
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In terms of pest information services, data constraints allow only for
a binary comparison. The agricultural research station data used in
estimating the insecticide production functions, and the parameters of the
loss expectation function can be interpreted as describing two extreme
cases: the "programmed" application pattern is typical for the farmer
who lacks pest infestation information, or is unable to interpret it.
These data can therefore be treated as describing the behavior of farmers
not utilizing a pest information program. The second data set, which des-
cribes the relatinship between insecticide use and yield for the policy to
spray whenever the infestation level reaches 25 percent, can be used to
represent the application pattern recommended by the typical pest infor-
mation program. These data can therefore be used to represent the farmer
enrolled in such a program and following its recommendations.
The comparison of insecticide use levels for these two types of farmers —
"uninformed" and "informed" — can be used to assess the potential of pest
information programs under the best of all possible circumstances. In the
real world, it would be unlikely that the farmer not enrolled in the pro-
gram would be completely oblivious to signs of insect infestation, just
as the participating farmer cannot be expected to follow recommendations
to the letter.
The analysis of the potential impact of crop insurance programs allows for
greater variation of policy options. Insurance programs affect the re-
lationship between the percentage of crop lost and monetary net income.
Three parameters are important in changing this relationship; these para-
meters describe the obligations of the insurer against the insured in case
of loss (assumed here to be attributable to insect damage). The first
parameter is the deductible, defined in terms.of some percentage of crop
lost. As long as the loss falls below the deductible percentage, the
farmer bears the full loss. If the loss excfeeds the deductible, the in-
surer may pay all or part of the loss beyond the (monetary) value of the
deductible. The second parameter is the coinsurance percentage which
specifies the portion of the loss born by the farmer himself. Finally,
a third parameter can be distinguished for the specification of insurance
options which describes the maximum loss (or minimum income) that the
36
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insured is guaranteed. Strictly speaking, this parameter results from a
combination of the other two. For example, if the insurer agrees to pay
the full value of the loss incurred minus the deductible, the maximum
possible loss is given by the value of the deductible. If a coinsurance
scheme without deductible is used, the maximum loss of the farmer is
the value of his maximum possible net income times the coinsurance frac-
tion (i.e., share of loss covered by the insurance program). In the spe-
cification of insurance options for the analysis here, the maximum loss
parameter has therefore not been used explicitly.*
The effect of the coinsurance factor (c) and the loss deductible (D) on
the relationship between percentage loss and net income described in
Equation (2) can be shown as follows:
7 =
Pv (1 - c-s)Y* - TC - pvX - p. for s <_ D;
I A I
py (1 - c'-s) Y* - TC - pxX - pjf for s > D.
(3)
where c = coinsurance fraction up to deductible;
c1 = coinsurance fraction beyond the deductible;
p = insurance premium.
These specifications have been used in the simulation model to describe
alternative insurance options.
The simulation analysis focuses on a total of seven insurance options,
including the no-insurance alternative. The options considered are "pure"
cases, that is, either coinsurance or deductible. However, the decision
model (and the simulation routine) can be used to examine more complex
options and combinations. The six effective insurance alternatives have
been specified as follows:
• 50% coinsurance, with the insurer and the insured each
bearing one-half of any loss incurred because of insect
damage; the annual premium cost required for full cost
recovery has been estimated at $34.00 per acre covered;
*The maximum loss parameter could be useful separately in the specifica-
tion of more complex insurance schemes, such as a deductible, plus some
coinsurance arrangement beyond the deductible up to a maximum amount to
be born by the insured, and full coverage beyond that point. In the
present analysis, the insurance options considered are simpler than that.
37
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• full coverage of the loss incurred beyond a deductible
of:
0%; premium estimated at $69.00 per acre;
10%; premium estimated at $67.00 per acre;
20%; premium estimated at $54.00 per acre;
25%; premium estimated at $43.00 per acre;
• the insurance option currently offered by the Federal
Crop Insurance Corporation; this option has been in-
terpreted as full loss coverage beyond a deductible
of 40%. This interpretation is the most appropriate
approach to translate the provisions of the insurance
services offered into the specification used here.
The annual premium per acre amounts to $32.00.
The annual premium payments required for full cost recovery under the
hypothetical insurance options have been estimated on the basis of the
total cost of indemnities to be paid, given historical loss distributions
for cotton producers due to insect damage.
The analysis of the impact of insurance programs on insecticide usage in
cotton production includes an assessment of the effects of price (premium)
variations through subsidies paid by the Federal government. Five sub-
sidy options have been used in the analysis; in addition to full-cost
pricing (zero subsidy), the simulation analysis considers reductions in
premium costs to the farmer by 10, 25, 50 or 100 per cent.
These specifications establish the background for the discussion of the
results of the simulation experiments. This discussion focuses first on
the comparison of insecticide use patterns for "uninformed" and "informed"
farmers. This comparison also provides some insight into the procedures
involved in obtaining the expected net utilities for each alternative con-
sidered. The discussion then proceeds to an examination of the impact of
insurance alternatives, based on the maximum expected utility for each
insurance/subsidy combination. In interpreting the figures displayed, it
is important to realize that the expected utilities are expressions of
relative preferences only. The numerical values as such are unimportant;
they certainly do not figure in this form in the farmer's decision making
process. Relevant to the analysis are the values of the expected utilities
relative to each other.
38
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IMPACT OF INFORMATION PROGRAMS
Table 4 displays the expected net incomes and associated expected utilities
for each of the nine insecticide application levels considered, both for
the "uninformed" and the "informed" farmer. The comparison of these data
shows clearly that expected net incomes are generally higher for the "in-
formed" farmer; the differences are substantial, reaching a maximum at the
15-pound application level ($43.30).
Correspondingly, expected utilities are generally higher for "informed"
farmers. At all application levels, knowledge of the most appropriate
application pattern would make the farmer better off. The only exception
to this pattern is the maximum application level (40 pounds); this result
is partially explained by the curvature of the quadratic production func-
tion for the "informed" farmer. In general, though, the subscription
charge of $3.00 per acre for participation in the pest management informa-
tion program is more than offset by increases in application efficiency.
The comparison of expected utilities for different levels of insecticide
application indicates that the optimal action (application level) for the
"uninformed" farmer is 35 pounds. It is interesting to note that ex-
pected utilities reach a maximum at a different application level than
expected net incomes. In other words, the risk factor at 30 pounds (for
which expected net income reaches a maximum) is sufficiently high to in-
duce the "uninformed" farmer to prefer the next higher application level,
even though it yields a lower expected net income.
In the case of the "informed" farmer, both expected net income and ex-
pected utility reach a maximum at 25 pounds. In this instance, a de-
cision rule based on the maximization of expected net income would yield
the same decision (application level) as the optimization of income/risk
combinations. This result suggests that participation in a pest manage-
ment information program lowers the associated risk sufficiently to en-
courage the farmer to forego additional applications whose only function
is the reduction of risk. In other words, pest management information not
only increases the efficiency of insecticides, but it also reduces the need
to use them as an "insurance" against risk.
39
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Table 4.. EXPECTED NET INCOMES AND UTILITIES WITH
AND WITHOUT INFORMATION PROGRAMS
Programmed Application Following Recommendations
(Without Information Program) of Information Program
Pounds of Insecticide
per Acre
0
5
10
15
20
25
30
35
40
Expected
Net Income
Per Acre
- $30.00
- $10.60
3.30
17.30
28.40
34.00
39.50
39.20
36.50
Expected
Utility
84.4
87.2
89.2
91.1
92.6
93.5
94.3
94.5
94.4
b
Expected
Net Income
Per Acre
$ 0.60
22.90
39.50
50.60
56.20
59.00
54.90
46.40
33.50
Expected
Utility
88.6
91.5
93.5
94.9
95.7
96.2
96.1
95.4
94.2
a The maximum expected net income per acre is achieved by using 33 pounds
of insecticides per acre without information programs
b Using 23 pounds per acre with information programs yields the maximum
expected income.
40
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The comparison of the optimal insecticide application level for the two
types of farmers indicates that complete compliance with information pro-
gram recommendations could reduce insecticide use by as much as 10 pounds
*
per acre, a reduction of almost 30 per cent. This reduction would be ac-
companied by an increase in the efficiency of cotton production. There are
no direct costs to the public, since the simulation assumes full-cost pric-
ing ($3.00/acre) for information services. Universal acceptance of infor-
mation program recommendations therefore would result in an overall increase
of resource efficiency.
A caveat is in order concerning this interpretation. The amounts of in-
secticides selected under the specifications of the simulation model are
high (roughly 10 pounds) compared to average usage patterns. It is likely
that these differences between actual and hypothetical usage patterns can
be attributed to the data used in deriving the parameters of the loss ex-
pectation functions. Since these data were obtained under experimental
conditions, they may represent a somewhat atypical situation. However,
even if the absolute amounts may be overstated, the relative impact of
pest management information programs indicated by the results of the simu-
lation experiments are representative of the gains reported by existing
pest information programs.
The potential benefits of participation in a pest management information
program are sufficiently high to raise the question why adoption is not
universal as yet. The probable explanation of the lack of universal parti-
cipation is that the fanner is uncertain of the gains from adoption. This
contention is supported by the experience of existing programs, which have
witnessed widespread acceptance after initial success. The farmer finds
himself in a situation analogous to that of the potential adopter in the
literature on the diffusion of innovation. This aspect is explored further
in Section VI.
This potential insecticide use reduction compares favorably with the re-
sults reported in our discussion of existing pest information programs
and is identical to the maximum reduction attained.
41
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IMPACT OF CROP INSURANCE PROGRAMS
Tables 5 and 6 present composite pictures of the outcomes of the simulation
experiments for alternative crop insurance options for both "uninformed"
and "informed" farmers. The individual entries in the tables specify the
maximum expected utility the farmer can achieve under each insurance/sub-
sidy combination; the figures in parentheses give the amount of insecti-
cides (in pounds per acre) that would maximize expected utility. For the
"uninformed" farmer, the potential of crop insurance as a viable policy
option to reduce insecticide usage appears extremely limited. At subsidy
levels of less than 50 per cent, only one insurance option would be pre-
ferred over no insurance, namely the full loss coverage with a zero de-
ductible. This option is of course somewhat hypothetical; in essence, it
is an income maintenance program for cotton farmers. Regardless of the
level of loss incurred, the farmer is assured of the maximum income pos-
sible. Since the value of the expected loss exceeds the premium (at any
level of subsidy), the farmer would of course substitute this insurance
program for the use of insecticides. For practical purposes, though, this
insurance alternative does not appear feasible; it would be extremely in-
efficient from a social point of view.
The same holds essentially for the other options involving full loss
coverage beyond a given deductible. Since they tend to induce the farmer
to stop using insecticides altogether, they are likely to create serious
inefficiencies in social resource allocation* The two remaining options,
50% coinsurance and FCIC, become attractive to the farmer only if they
are provided free of charge, i.e. at a 100% premium subsidy. These op-
tions would lead to a reduction of insecticide use of five pounds per acre.
The cost of this reduction to the public would be $32 to $34 per acre; di-
viding the required subsidy by the f iye pound insecticide reduction achieved
would yield a public cost figure of roughly $6.60 per pound of insecticide
use eliminated. Although the social costs of insecticide use are unknown,
detrimental side effects would have to be extremely high to warrant this
level of expenditure.
42
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Table 5. MAXIMUM EXPECTED UTILITIES FOR UNINFORMED APPLICATION PATTERNS
Full Loss Coverage With Deductible
Insurance Option ; None
($0)
Premium Subsidy
in Per Cent
0 94.5
(35)
10 94.5
(35)
25 94.5
(35)
50 94.5
(35)
100 94.5
(35)
50% Coinsurance
($34)
92.3
(30)
92.5
(30)
93.0
(30)
93.7
(30)
95.0
(30)
0%
($69)
95.1
(0)
95.7
(0)
96.5
(0)
97.7
(0)
100.0
(0)
10%
($67)
93.0
(0)
93.6
(0)
94.4
(0)
95.8
(0)
98.2
(0)
20%
($54)
92.1
(0)
92.6
(0)
93.3
(0)
94.4
(0)
96.5
(0)
25%
($43)
92.2
(0)
92.6
(0)
93.1
(0)
94.0
(0)
95.7
(0)
FCIC
($32)
92.3
(30)
92.6
(30)
93.0
(30)
93.7
(30)
95.0
(30)
aAnnual premium in parentheses.
-------
Table 6. MAXIMUM EXPECTED UTILITIES FOR INFORMED APPLICATION PATTERNS
*>.
•tfc
Full Loss Coverage With Deductible
Insurance Option None
($0)
Premium Subsidy
in Per Cent
P 96.3
(25)
10 96.3
(25)
25 96.3
(25)
50 96.3
(25)
100 96.3
(25)
50% Coinsurance
($34)
93.9
(25)
94.1
(25)
94.6
(25)
95.2
(25)
96.5
(25)
0%
($69)
94.9
(0)
95.4
(0)
96.2
(0)
97.5
(0)
99.8
(0)
10%
($67)
93.0
(0)
93.5
(0)
94.4
(0)
95.7
(0)
98.1
(0)
20%
($54)
92.5
(10)
93.0
(10)
93.6
(10)
94.7
(10)
96.8
(10)
25%
($43)
93.2
(15)
93.5
(15)
94.1
(15)
94.9
(15)
96.6
(15)
FCIC
($32)
93.8
(25)
94.0
(25)
94.4
(25)
95.0
(25)
96.3
(25)
No subsidy for information services; full-cost price of $3.00 per acre.
Annual premium in parentheses.
-------
For the "informed" farmer, the results of the simulation experiments sug-
gest that the no-insurance option is preferable to any other one, as long
as the premium subsidy offered is less than 50 per cent. At that subsidy
level, the "informed" farmer would prefer the full loss coverage with a
zero deductible. However, this option again would induce him to abandon
insecticides completely; as in the case of the "uninformed" farmer, this
insurance alternative would fail to pass the feasibility test.
For a complete subsidization of insurance premium costs, the farmer would
prefer any insurance over the no-insurance option. However, neither the
50% coinsurance scheme nor the FCIC alternative would alter insecticide
use. These options would therefore serve only to raise the net income of
the farmer without lowering the social costs of insecticide use. The full
loss coverage with a deductible of 10 per cent would lead to a complete
elimination of insecticides, while the 20 and 25 per cent deductible alter-
natives would induce reductions by 15 and 10 pounds, respectively. These
results indicate that the "informed" farmer reacts much more flexibly to
variations in insurance provisions. Full loss coverage with deductibles
of 20 and 25 per cent would create substantial reductions of insecticide
use without eliminating it completely. However, the subsidy cost of these
reductions is substantial; per pound of reduction, the 20 per cent de-
ductible option would require a subsidy of $3.60, while the 25 per cent
deductible would require $4.30 per pound.
CONCLUSION
The simulation experiments lead to three major conclusions concerning the
relative effectiveness of pest management information and crop insurance
programs:
1. Pest information programs can lead to a
reduction of insecticide use in cotton production
of up to 30%; this reduction is accompanied by sub-
stantial improvements in production efficiency*
leading to higher expected net incomes and higher
expected utilities.
45
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2. In the absence of information programs, crop in-
surance programs could reduce insecticide use
only at a high cost to the public; in most cases,
the farmer would substitute insurance for insecti-
cides, which would entail a number of indirect
costs to society, such as higher commodity prices
or shortages.
3. For the "informed" farmer, full loss coverage
beyond deductibles of 20 or 25 per cent would
reduce insecticide usage at a relatively high
price to the public. However, a full substitu-
tution would not occur.
These findings of the simulation analysis form the background for the
discussion of the potential of information and insurance programs to
"reach" the farmer, i.e., to alter the inputs into his decision process.
46
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SECTION VI
DETERMINANTS OF PROGRAM PARTICIPATION
INTRODUCTION
The results of the decision-theoretic analysis indicate that fanner be-
havior is sensitive to variations in insurance premium levels. In the
case of information programs, variations in price did not show any ef-
fects on relative preferences;* application according to need would be
preferred at any price up to the price level required for full cost re-
covery. However, the theoretical analysis fails to clarify the response
of farmers under conditions of uncertainty.
In order to arrive at an assessment of the relative potential of the two
types of programs, it is necessary to review their experience under actual
operating conditions. To what extent have they been able to gain the
cooperation of farmers? The data available for examining this question
are rather limited, which constrains the scope of the empirical analysis
to some extent. For example, the results of the simulation model indi-
cate that "informed" farmers differ from their "uninformed" counterparts
with respect to their willingness to purchase insurance services. This
aspect cannot be explored here, since data are lacking that would describe
both subscription to information services and purchase of insurance cove-
rage. Even so, the empirical analysis of farmer response to variations
in program characteristics provides some guidance to the development of
broad policy recommendations.
PURCHASE OF CROP INSURANCE COVERAGE
Microeconomic theory implies that the quantity of a good or service pur-
chased increases with decreasing price, provided all other factors in-
fluencing demand are held constant. Since qualitative variations of
crop insurance programs are currently limited, the analysis of the de-
terminants of participation here focused on the relationship between
the insurance coverage purchased and the price of that coverage.
*
Because the relative preferences were not altered, these results are not
reported.
47
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The sample for the analysis was drawn from cross-section data for 1972
on counties participating in both the Federal Crop Insurance Corporation
program and USDA Pest Management Programs. The data are limited to 1972,
since it was the first year that an effective public pest management pro-
gram existed for cotton. Although some public and private programs were
in existence prior to 1972, they operated at a small scale; comparable
data for different programs are lacking.
The FCIC provided previously unpublished cotton insurance data on a per
county basis. These data include:
• acres insured,
• acres eligible for insurance,
• liability,
• premium rates,
• indemnity payments,
• loss ratios.
This information allows for a calculation of the share of eligible acres
insured, the average liability per acre, and the premium rate per dollar
of coverage. These variables were used in the statistical analysis.
To estimate the cotton farmer's responsiveness to price variations in terms
of different premium levels, ordinary least squares estimation techniques
were applied to a single-equation demand model. The demand equation for
crop insurance coverage expresses the amount of insurance coverage pur-
chased per acre as a function of the cost to the farmer per dollar of that
coverage. The functional form chosen for the analysis is the multiplica-
tive one:
where C = dollars of coverage purchased per eligible
cotton acre in the county;
p = price of insurance per dollar of coverage
in the county;
a. = coefficients (i = 0, 1).
i
48
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The linear regression analysis used the logarithmic transformation of
Equation (4). The estimation based on data for 72 counties yielded
the following parameters:
In C = 4.16 - 1.71 In p ,
(-4.12) <5>
where the figure in parentheses denotes the t-statistic of a,. The
explanatory power of this regression equation is somewhat disappointing;
2
the R is rather small (.19). However, the t-statistic indicates that
the estimated value of a is significantly different from zero at the
99% confidence level. Also, cross-section investigations of this nature,
where a number of environmental variables are excluded, cannot be ex-
pected to have strong explanatory power.
This equation implies that a Federal subsidy of, say, 10 percent on
the cost of the premium would induce a 17 percent increase in the amount
of insurance coverage purchased per acre of cotton eligible for all-
risk FCIC insurance. Thus, U. S. cotton farmers are far less responsive
to a premium subsidy than their Canadian counterparts. In a study of the
experience with crop insurance in the Canadian Province of Manitoba it was
found that a 25 percent premium subsidy raised participation from 10
to 60 percent of eligible acreage. (The initial 10 percent rate is similar
to the current U. S. participation rate.) Three possible explanations of
the discrepancy are: (1) Canadian farmers are producing different crops
(principally wheat); (2) other price support and income maintenance
programs do not exist; and (3) coverage is extended to a greater portion
of the potential loss.
It is difficult to relate these results to the findings of the simulation
analysis which indicates that farmers would adopt insurance (or at least
feasible insurance options) only at a 100% subsidy. One factor should be
kept in mind, though. A more important difference between the analysis here
and the simulation analysis concerns the character of the insurance
coverage. The FCIC coverage includes all risks, while the simulation
49
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analysis was based on the assumption that insurance coverage would be
specific to insect damage. It is possible that these differences account
for differences in behavior patterns with respect to the purchase of in-
surance coverage. These differences could conceivably be reconciled by
regarding the coverage of risks other than insect damage by the FCIC,
insurance as an indirect "premium subsidy," which would induce farmers
to purchase this coverage. However, without evaluating the expected
values of other risks, this interpretation cannot be tested.
The statistical analysis included a number of other factors that failed
to show significant relationships to the dependent variable. .The theo-
retically most interesting aspect, demand effects in the insurance market
-t ' • \ i :
variable in explaining subscription to FCIC crop insurance.
SUBSCRIPTION TO PEST INFORMATION SERVICES
The simulation analysis and the review of currently operating pest infor-
mation programs suggest that the farmer is likely to benefit substantially
from participation in information programs. However, participation is by
no means universal as yet. The likely reason for this phenomenon is that
farmers cannot know the likely benefits of participation with certainty.
Variations in the subscription price may therefore influence the decision
of the farmer. In addition, it is reasonable to expect that the perceived
quality of pest management information programs affects the farmer's
assessment of likely benefits. Finally, it is conceivable that the price
of substitutes to information services, such as insurance, influences the
demand for pest management information.
These factors have been tested in a demand equation for information ser-
vices. The pest management data were obtained from the Department of
Agriculture and cooperating state pest management programs for cotton.
As observed above, 1972 was the first year the program had reached a
sufficient magnitude to permit any statistical analysis of cross-section
data. This concentration on the first year of full operation may affect
50
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the results of the regression analysis. This possible bias should be
taken into account in interpreting the estimates obtained.
Perhaps the most interesting outcome of the statistical analysis of the
demand for pest information services is the failure of proxy variables
for service quality to perform satisfactorily in explaining subscription
patterns. The proxies used included the ratio of supervisors to scouts,
since closer supervision should be an important component of higher-
quality services; the acreage covered per scout, since smaller acreage
should permit more thorough scouting and greater client contact; and
the number of fields per scout as a measure of the average workload and
travel required. The poor performance of these quality proxies can be
attributed to two reasons: (1) they tend to correlate highly with the
price of information services, and (2) they frequently reflect regional
differences in production conditions, e.g., scale of cotton production,
rather than actual quality differences.
The demand equation that performed best in the statistical analysis is
a multiplicative model incorporating prices for both information services
and insurance coverage as independent variables:
w = ao pw *i (6)
where W = the ratio of cotton acres participating in a
pest management information program to total
cotton acres in the county;
p = the per acre cost to the farmer of subscribing
to information services in a particular county;
p = the price of insurance per dollar of coverage
in the county;
a. = parameters (i = 0, 1, 2).
The parameter estimates based on the logarithmic form of this demand
equation are significantly different from zero; however, the explanatory
2
power of the model is somewhat limited, as indicated by an R of .29 for
a sample of 43 observations:
In W = .26 - 1.92 In p - .96 In p
I (7)
(-3.41) (-2.24)
Figures in parentheses denote the t-statistics for the parameter estimates.
51
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The results of the analysis would imply that a subsidy for insurance
premiums would lead to an increase in the share of total cotton acreage
participating in the pest information program, the response elasticity
being close to -1.0. However, this result should be treated with some
caution. First, the approach used here to incorporate the complementary
relationship between insurance and information into a single-equation
framework may not be appropriate, possibly introducing a bias into the
estimation procedure. Secondly, the price of insurance may be a proxy
for other variables not included in the analysis. For example, Carlson
has found that larger farmers used both more insurance and more pesti-
cides than smaller-scale operators.* It is possible that the operators
of larger farms, who are frequently better trained, are more likely to
realize the value of both information and insurance services offered. In
this interpretation, the insurance price effect in the demand equation
for information services would be attributable to the effects of farm
size variations and the associated variations in educational background
and training of farm operators. It is reasonable to conclude, therefore,
that the direction of the impact of a subsidy on insurance premiums on
the demand for information services is correct, but that its magnitude is
uncertain.
The estimates reported in Equation (7) also imply that the direct price
elasticity of the demand for information services is approximately -1.9;
this figure does not change significantly, if the price of insurance
coverage is dropped from the equation. A 10 per cent decrease in the cost
per acre scouted would lead to a 19 per cent increase in the share of
total cotton acreage participating in the pest management program. Because
the elasticity analysis was based only on regions conducive to scouting,
this elasticity is of course only relevant in such regions. Some regions
are not amenable to scouting, and of course the analysis does not apply
in these cases.
* Unpublished research by Professor Gerald Carlson; in reviewing the ana-
lysis reported here, he indicated the need for caution in interpreting
the cross-price elasticity estimate.
+ Another possibility is of course that the provisions of the FCIC in-
surance program ("good pest management") constitute an incentive to
subscribe to information services.
T Source: private conversation with Professor John Thomas.
52
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The problems associated with the interpretation of the cross-price elasticity
of the demand for information services suggests that a different approach
may be fruitful, based on the interpretation of the participation in pest
management programs as an innovation in cotton production. Research on
the diffusion of innovation, summarized by Brown [ 2 ], has focused on
the interaction between "adopter" characteristics (e.g., education, farm
size, operating efficiency) and policy characteristics of the "diffusion
agency"- However, an application of this approach to the analysis of the
adoption patterns for pest management programs goes beyond the scope of
this study.
CONCLUSIONS
The results of the analysis of the responsiveness of farmers to variations
in the prices of insurance and information services complement the simula-
tion analysis of the potential impact of such programs. Although FCIC
insurance utilization is responsive to price variations per unity of cover-
age, the simulation experiments suggest that little change in insecticide
use can be expected. Subsidizing the current FCIC program therefore would
be unlikely to bring about significant reductions in insecticide use; in
addition, the stipulations of the program in its current form do not
directly encourage such reductions.
Pest information utilization appears to be sensitive to variations in the
cost of subscription to the farmer. This result is important, since it
provides an impression of the assessment of relative benefits of parti-
cipation by the farmer. The findings of the demand analysis for pest
information, coupled with the results of the simulation experiments and
available data on the program experience, demonstrate the potential of
providing information subsidies to encourage the adoption of pest infor-
mation programs. Such an approach is likely to yield a net social benefit
in the form of reduced damages to the environment.
53
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SECTION VII
POLICY IMPLICATIONS
INTRODUCTION
The nature of this study is largely exploratory. Its principal value lies
in demonstrating the potential of a comprehensive framework for evaluating
policy alternatives to regulation and tax/subsidy schemes in protecting the
environment from harmful effects of pesticide use. The methodological struc-
ture developed here reflects the functions of the policy options studied,
pest information and crop insurance programs. It organizes theoretical and
empirical analysis around a conceptual model of the farmer's pesticide use
decision process. This approach is shown to be an effective tool for the
assessment of new policy initiatives.
The application of the methodological framework to the insecticide problem
in cotton production, however, goes beyond the mere demonstration of this
approach. The theoretical and empirical evidence organized under this
structure allows for an assessment of "real" policy alternatives. This
section summarizes the findings of the analysis focusing on the implica-
tions for new policy initiatives geared toward the reduction of environ-
mental damages associated with insecticide use in cotton production. The
discussion here proceeds from a summary of the major findings of the deci-
sion analysis to an assessment of the expansion potential of currently
existing pest information and crop insurance programs.
MAJOR FINDINGS
The simulation results of the potential insecticide use of cotton pest in-
formation and crop insurance programs indicate that improved information
can cause significant reductions in application levels without adverse eco-
nomic effects to the farmer. The 30 percent insecticide use reduction re-
sulting from the introduction of pest information in the simulation model
is corroborated by available evidence regarding the experience of the USDA
Pest Management Program.
54
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In contrast, the potential of crop insurance programs to reduce insecti-
cide use among farmers who do not participate in pest information programs
appears to be fairly limited. As soon as the risk reduction associated
with the purchase of insurance coverage reaches a certain level, the simu-
lation model yields a "radical" solution: the farmer would simply substi-
tute (heavily subsidized) insurance for insecticide use. Such a result is
feasible on economic grounds. For insurance options where the farmer as-
sumed a greater share of the risk without the benefit of pest information,
he would reduce his insecticide use somewhat, provided the subsidy reaches
a sufficiently high level.
The potential impact of insurance programs appears somewhat better for farm-
ers who do participate in pest information programs. In these cases, appro-
priate subsidies on insurance premiums can induce substantial reductions
in insecticide use without causing a complete abandoning of insecticides.
However, the cost of these reductions is substantial.
While the available evidence for pest information programs allows for a
crude verification of the simulation results, available data on insurance
programs fail to provide a basis for such a check. The most widespread
crop insurance program in existence, provided by the Federal Crop Insurance
Corporation, is an all-risk insurance. Therefore, even if data had been
gathered on insecticide use by participating farmers and others, the com-
parison with the results of the simulation experiments (which assumed in-
surance specific to the insect damage) would be misleading. In any case,
the required data are simply not available. The assessment of crop in-
surance program potential thus rests on the simulation analysis alone.
The examination of farmer responsiveness to price variations in the insur-
ance and information programs shows that the price elasticity of demand is
comparable for pest information and crop insurance programs: slightly less
than -2.0. These results indicate that a 10 percent subsidy of the farm-
er's participation cost would lead to a 20 percent increase in the overall
participation rate. Given the relatively low cost of pest information
services per acre, combined with their effectiveness in reducing insecti-
55
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cide use for participating farmers, a policy focusing on subsidized pest in-
formation services appears to be most promising. Since the simulation ex-
periments indicate that farmers accrue a net benefit, even if they pay the
full cost of pest information services, it is possible that these subsidies
can be phased out, once widespread adoption has been achieved.
This summary of the major findings of the study provides the background
for an exploration of the potential for expanding currently operating
programs.
POTENTIAL FOR EXPANSION OF FEDERAL CROP INSURANCE
If, contrary to the simulation results of this study, it is decided to
expand insurance, the following issues are relevant. Bailey and Jones
[1] observe that participation by cotton producers in the FCIC program
varies widely by region. Sixteen percent of the total eligible cotton
acreage was insured by the FCIC in 1968. Among regions, the percentage
ranged from half the cotton acreage in Alabama to cover a fourth in Arizona
and New Mexico to a tenth in Mississippi and Arkansas. The reasons for these
variations are not immediately obvious, three factors appear most important:
local FCIC sales efforts;
historical relationship of premiums paid and
indemnities recovered;
farmer's assessment of his risk and FCIC's
ability to cover his potential loss.
These factors suggest areas of greatest potential for increasing partici-
pation in crop insurance, should this strategy be adopted as a (temporary)
complement to expanding pest information services.
One potential modification of the current crop insurance structure deserves
special attention. FCIC insurance should cover cotton yield losses in-
curred as a result of the producer's decision to spray only as recommended
by pest management personnel. Such a provision could be a powerful incen-
tive to comply with pest management recommendations. The -incentive could
even be increased by stipulating the adoption of integrated pest manage-
ment practices, including spraying according to scouting information, as
a condition for eligibility. The provisions of the Crop Insurance Act
56
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can be interpreted to establish such a criterion. The Act rules out losses
due to "failure of the insured to follow established good farming practices."
The decision on the operational definition of."established good farming
•practices" is left to local committees. These committees are likely to
accept local production practices that are used by the majority, or the
leaders, of local cotton growers. It is therefore possible that compliance
with pest management recommendations is regarded as "established good farm-
ing practice," Under this interpretation, no legislative changes would be
required to use the FCIC program to encourage participation in pest infor-
mation programs.
POTENTIAL FOR THE EXPANSION OF PEST INFORMATION PROGRAMS
The apparent effectiveness of cotton pest information programs in reducing
insecticide use without adverse economic effects on producers suggests the
need to substantially increase the total acreage scouted. A Federally spon-
sored pest information service would supplement existing scouting programs.
Farmers may shift from other scouting programs or from scouting their own
fields to such a program if the cost of subscription is sufficiently low.*
However, the acreage covered by non-Federal programs would not likely de-
crease because of the rapid expansion of the overall "market" for pest
information services
An assessment of the expansion potential of Federal pest information ser-
vices requires answers to a number of questions: How many additional cot-
ton acres are amenable to scouting? What would be the annual cost of an
expanded program. How many years would it take to realize such an expan-
sion? An exploration of these issues in discussions with pest management
personnel suggests the following conclusions:
• The total remaining cotton acreage that could be
covered by. an expanded program would range from
a minimum of approximately 5 million acres to a
maximum of about 9 million acres, out of the to-
tal of 13.5 million acres of cotton.
'A potential problem is the possibility of unfair competition with private
pest management services. One alternative would consist in subsidizing
farmers without regard to the source of their pest information and rec-
ommendations .
57
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Although our simulation results indicate that utili-
zation of information services is potentially pro-
fitable even in the absence of subsidies, the ex-
pansion of existing information programs would imply
continued subsidization, thus the Federal subsidy
required per acre would range from a minimum of $1.50
to a maximum of $4.00, depending on the level of ser-
vices provided, the cost of these services, farmer
contributions, and other factors.
The total Federal cost of an expanded program
would probably be about $15 million per year,
but could range from a low of $7 million to a
high of $37 million, dependent upon the acreage
covered, and the average subsidy per acre.
It would take from three to five years to expand
the program to cover the maximum acreage, because
of the need to recruit and train scouting manpower,
and to gain acceptance by farmers.
The procedures used in estimating the total acreage that could be covered
in an expanded Federal pest information program are illustrated in Table 7.
Basically, the approach has been to start with the total acreage in cotton
production and to subtract estimates of acreage that would be unlikely to
be included in a Federal program. In each case, a low and a high esti-
mate of the acreage likely to be excluded has been given.
For acreage covered by growers, consulting entomologists, and other non-
Federal pest information programs, current coverage has been used as a
minimum estimate, with a 50 per cent higher figure being used as the maxi-
mum. These estimates are based on discussions with pest management per-
sonnel. Areas with low infestation levels (such as the Texas Rolling
Plains) that make pest information services largely superfluous account
for as much as 25 per cent of total O. S. cotton acreage; estimates of this
acreage vary from 1.0 to 3.4 million cotton acres.
About one-half to one million cotton acres are farmed in small allotments
by growers whose marginal economic situation makes their participation
unlikely. Finally, 900,000 acres are already being scouted by Federal
pest information programs. The expansion potential therefore varies from
3.8 to 8.3 million cotton acres, corresponding to a total coverage between
4.7 and 9.2 million acres.
58
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Table 7. ALTERNATIVE ASSESSMENTS OF ACREAGE POTENTIAL AND
COST FOR FEDERAL INFORMATION SERVICES, COTTON
Millions of Acres
Low Alternative High Alternative
TOTAL U.S. COTTON ACREAGE 13.5 13.5
Less:
Acreage Scouted by:
Growers 1.7 1.1
Consulting Entomologists,
Chemical Industry, Gins, Etc. 2.7 1.7
Acreage where scouting uneconomic
due to low infestations 3.4 1.0
Acreage in small parcels or
farmed by independent farmers 1.0 0.5
Potential acreage to be scouted
by federal scouting program:
Already scouted .9 .9
Expansion potential 3.8 8.3
POTENTIAL TOTAL ACREAGE
IN FEDERAL PROGRAM 4.7 9.2
59
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At present, the data presented in Section IV imply a total subsidization
of the Cotton Pest Management Program in 1973 from public sources of $1.82
per acre. This average covers a wide variety of program approaches. Some
of the states provided participating farmers with field infestation data
only, and not with specific advice (other than general extension pamphlets)
on when to spray or what other pest control measures to take. Any improve-
ments in these programs may imply that the $1.82 subsidy would have to in-
crease substantially. If farmers are charged $1.00 per acre scouted or
less, the Federal subsidy required could be as high as $4.00 per acre under
a more comprehensive program.
However, certain developments are likely to reduce the costs of a scouting
program. Many expenditures currently made are investments in the establish-
ment and improvement of the program. A number of scouting programs have
been established on an experimental basis to determine whether it is pos-
sible to address some problem specific to the given county. In addition,
some "learning-by-doing" has taken place — with concomitant inefficiencies.
Finally, the uses of computerized reporting systems and data storage for
greater program efficiency are becoming better understood. If services
offered were not substantially expanded from the present average, subsidy
costs for pest information services might run closer to $1.50 per acre per
year.
Table 8 presents estimates of the total annual costs of an expanded
Federal pest information program under alternative assumptions about
acreage included and subsidy costs per acre. The low-acreage, low-cost
combination would cost about $7 million per year to operate at the local
level. (The estimates do not include the costs of administering the pro-
gram at the Federal level.) The costs might go as high as $36.8 million.
If we assume that information subsidies are necessary to widespread par-
ticipation in information services programs as a means of reducing insec-
ticide use, then the cost of this reduction to the public can be calcula-
ted; dividing the required subsidy by the insecticide reduction achieved
would yield a cost per pound ranging from $0.15 to $0.40.
60
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Table 8. ESTIMATED COSTS OF EXPANDED
FEDERAL PEST INFORMATION PROGRAM
_ , . _ . . , _ . Total Acreage in Federal Program
Federal Subsidy Cost 2 3
Per Acre 4.7 Million 9.2 Million
$1.50 $7.0 million $13.8 million
$4.00 $18.8 million $36.8 million
In addition to possible financial limitations, there are of course other
constraints on a rapid expansion of a Federal scouting program. Perhaps
the most important factor is manpower availability. Thus far, there has
been no difficulty in recruiting college students in fields such as bio-
logy or agriculture to work as scouts during the summer. However, in the
short run, there may be a ceiling level beyond which it would be difficult
to locate a sufficient number of qualified recruits. Another limiting
factor is the willingness of farmers to participate in the program. The
closer participation rates come to the satiation level, the more likely
are the remaining non-adopters to resist change. For these reasons, it
appears likely that a period of three to five years would be a reasonable
expectation for the maximum expansion of a Federally sponsored pest in-
formation system.
Program Delivery Systems
Several choices are possible in the institutional structure of the Federal
pest information program. These choices concern the role of the Federal
government, and the mix of responsibilities among government agencies,
organized grower pest control groups or cooperatives, and private sector
informations services. There are four major roles that the government could
play:
61
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* Directly administer a pest information service
through existing agencies or by organizing a
new agency for this purpose.
* Contract out the functions of an information
service to private sector consulting firms
or to grower organizations.
• offer subsidies to any organization that will
operate a pest information service or offer
subsidies to farmers who agree to participate
in scouting programs.
* P^ffeE informal assistance or encouragement to
those who will establish a pest information or
scouting program.
Any two or more of these functions can of course be combined. For example,
a Federally sponsored pest information service could administer certain
functions itself, and either subsidize, contract out, or provide informal
technical assistance to other organizations willing to perform complemen-
tary functions. Such combinations are common in the current Cotton Pest
Management Program, where many states train scouts, make recommendations
to farmers, and computerize field data, but leave the hiring and deploy-
ment of scouts to farmer groups.
Peat Information Quality
Although high correlations between quality proxies and prices of pest in-
formation services precluded an assessment of information program qualita-
tive characteristics on participation patterns, it is reasonable to postu-
late a positive effect. The following remarks concern the potential for
improving these characteristics.
Scout Supervision and Client Contact; The scout supervisor plays an im-
portant role in a pest information program. He can perform quality checks
on scouting reports, evaluate field data, and formulate recommendations
to farmers. A higher supervisor/scout ratio therefore is a potentially
important factor in gaining and maintaining the farmer's confidence in the
quality of the scouting. In addition, supervisors with fewer scouts are
likely to be more accessible to farmers, which increases the chances of
the farmers complying with recommendations. In 1972, the number of scouts
62
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per supervisor in the nationwide pest management application projects
ranged from 3 to 36, for an overall average of 11.5.
However, further research is required to determine the effects of patterns
of .supervision and quality of supervisors on the effectiveness of pest
information programs.
Scout Workload. The reliability of scouting information — as well as
that of resulting recommendations — is likely to be effected by the total
acreage or the number of fields assigned to each scout. Scout workloads
should therefore be regarded as a policy variable.
Nature of Recommendations to Farmers. Recommendations to farmer concern-
ing appropriate pest control measures can vary in three major respects:
• they may suggest the application of pesticides when
the infestation level is sufficient to predict any
reduction, or they may suggest applications only
when the cost of yield (or quality) losses because
of pest damage would exceed the cost of pesticide
applications;
• they may assume different allowances for error and
different degrees of risk aversity, and they may or
may not make these assumptions explicit to the
farmer;
• they may or may not include integrated pest management
advice as opposed to pesticide application recommenda-
tions alone. .For example, recommendations could be
made about biological pest control practices, as well
as cultural practices related to pest control.
Choices among these variations in the type of recommendations constitute
major policy variables.
OUTLOOK
The methodological framework developed in this study offers a flexible
approach to evaluate,policy alternatives in the field of environ-
mental protection? reduced damages from harmful pesticides used in agri-
culture. The further development of this methodology can be extremely
useful in developing a more differentiated set of policies for a pollu-
tion problem that is more difficult to handle than those created by point
63
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sources. Applications of the methodology to other types of pesticides
and other crops would provide insights into necessary refinements of the
current framework.
In addition, perhaps the weakest link of the approach in its present
form is the connection between the potential impact of "pure" policy
options and the means of realizing this potential. While it is unlikely
that the development of a more complex model that attempts to incorporate
all aspects of farm operations would be cost-effective, a number of
possibilities exist for expanding the conceptual framework and the re-
sulting model. This expansion is perhaps most important with respect to
the analysis of insurance options, where differences in coverage (specific-
risk vs. all-risk) appear to have a significant effect on the results of
the analysis.
64
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SECTION VIII
REFERENCES
1. Bailey, W.R. and L.A. Jones. Economic Considerations in Crop Insurance.
ERS, USDA, Washington, D.C. ERS-447. August 1970. 87 p.
2. Brown, L.A. Diffusion Processes and Location. A Conceptual Framework
and Bibliography. Philadelphia, Regional Science Research Institute,
1968. 177 p.
3. Carlson, 6.A.Decision Theoretic Approach to Crop Disease Prediction
and Control. American Journal of Agricultural Economics. 52:216-223,
May 1970.
4. Cooke, F.T. The Effect of Restricting DDT and Chlorinated Hydrocarbons
on Commercial Cotton Farmers in the Mississippi Delta. In: Economic
Research for Policy Decisionmaking. (Proceedings of a Symposium) ERS,
USDA, Washington, D.C. April 27-29, 1971. p. 123-136.
5. Cooke, F.T., J.H. Berry, and A.S. Fox. Economic Effects of Restricting
the Use of DDT on Cotton. Testimony Before EPA Public DDT Hearings.
Washington, D.C. October 1971.
6. Davis, V., et al. Economic Consequences of Restricting the Use of
Organochlorine Insecticides on Cotton, Corn, Peanuts, and Tobacco. ERS,
USDA, Washington, D.C. Agricultural Economic Report No. 178. March 1970.
51 p.
7. Dixon, O., P. Dixon, and J. Miranowski. Insecticide Requirements in an
Efficient Agricultural Sector. Review of Economics and Statistics.
55(4):423-432, November 1973.
8. Eichers, T., et al. Quantities of Pesticides Used by Farmers in 1966.
ERS, USDA, Washington, D.C. Agricultural Economic Report No. 179.
April 1970. 61 p.
9. Ganyard, M.C. and G.B. Worley. North Carolina Insect Pest Management
Program. 1973 Yield Study. Preliminary Report. North Carolina State
University. (Unpublished Manuscript. Undated.) 9 p.
10. Halter, A.N., and G.W. Dean. Decisions Under Uncertainty With Research
Applications. Cincinnati, O., Southwest Publishing Co., 1971. 266 p.
11. Heady, E.O., and J.L. Dillon. Agricultural Production Functions. Ames, la.,
Iowa State U. Press, 1961. 667 p.
12. Heady, E.O., and L.G. Tweeten. Short-Run Corn Supply and Fertilizer
Demand Based on Production Functions Derived from Statistical Data; a
Static Analysis. Agricultural and Home Economics Experiment Station,
Iowa State University, Ames, la. Research Bulletin No. 507. June 1962.
65
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13. Hogg, R.V., and A.T. Craig. Introduction to Mathematical Statistics.
Second Edition. New York, N.Y., Macmillan, 1967. 383 p.
14. Huffman, W.E. The Contribution of Education and Extension to Dif-
ferential Rates of Change. (Unpublished Ph.D. Thesis) University of
Chicago, 1972.
15. Jones, L.A. Insuring Crop and Livestock Losses Caused by Restricted
Pesticide Use: An Appraisal. ERS, USDA, Washington, D.C. ERS Publication
No. 512. January 1973. 7 p.
16. Pimentel, D., and C. Shoemaker. An Economic and Land Use Model for
Reducing Insecticides on Cotton and Corn. Department of Entomology,
Cornell University, Ithaca, N.Y. Report No. 72-3. December 1972.
35 p.
18. Sutherland, J.G., G.A. Carlson, and D.M. Hoover. Cost of Producing
Cotton in the Southeast: 1966. Department of Economics, North
Carolina State University at Raleigh, Raleigh, N.C. Economics
Information Report No. 25. October 1971. 53 p.
19. Texas A&M University. Impact of Drastic Reduction in the Use of
Agricultural Chemicals on Food and Fiber Production and Cost to the
Consumer. Special Report of College of Agriculture. Texas A&M Univer-
sity. College Station, Tx., July 1970. 62 p.
20. Thomas, J.G. A Review of the 1972 Cotton Pest Management Programs.
Extension Service, Phoenix, Az. Summary Proceedings of the 1973
Beltwide Cotton Production Mechanization Conference, January 11-12,
1973. January 1973. 31 p.
21. USDA. Crop Production. Crop Reporting Board. Statistical Reporting
Service, Washington, D.C. November 1973.
22. USDA. Crop Production. Crop Reporting Board. Statistical Reporting
Service, Washington, D.C. June 1973.
23. USDA. 1972 Benefit Summaries of Pest Management Projects. Office of
Director of Pest Management Programs, Extension Service, Washington,
D.C. (Unpublished Manuscript. Undated.)
24. Watson, T.F., and M.C. Sonyers. Comparison of Insecticide Application
Schedules for Control of Cotton Insects. Journal of Economic Entomology.
58: 1124-1127, December 1965.
66
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APPENDIX A
THE MATHEMATICAL STRUCTURE OP THE SIMULATION MODEL
This appendix describes the mathematical structure of the decision-theoretic
model that has been used in the simulation experiments to determine the ef-
fects of pest management information and crop insurance programs. The dis-
cussion proceeds from the presentation of the general structure of the
model to a brief examination of the problems involved in preparing the
model for digital-computer simulation.
The core of the decision-theoretic model is the conditional loss expectation
function for a given level of pesticide use. Basically, the loss expectation
function describes the probabilities that the farmer assigns to a given loss
level, expressed as the percentage of maximum yield lost because of the inci-
dence of crop pests. This function is a probability density function (p.d.f.)
whose parameters depend on the level of pesticide use. For the first part of
the analysis up to Equation (A.8) — the functional form of this p.d.f. need
not be specified.
Expectations of percentage losses affect the pesticide use decision of the
farmer only through their relation to expectations concerning the net in-
come associated with alternative pesticide application levels. The func-
tional relationship between the proportion of crop lost and net income per
acre is given by:
(A.I) y = p (1 - s) Y* - TC - p^,
where y = net income, $
p = price per unit of the crop, $
Y* - maximum possible yield per acre, Ibs.
TC = total cost of production (except pesticide cost)
per acre, $
p = price per pound of pesticide, $
J»
X = pounds of pesticides applied per acre, Ibs.
S = fraction of crop lost due to insect damages.
Given the parameters of the loss expectation functions for different levels
2
of pesticide applications, i.e., means (P ) and variances (a ), the parameters
67
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of the net income expectation functions can be calculated directly from
Equation (A. 1):*
py (i - v8) Y* - TC - PXX,
(A. 2)
The mean and the variance of the net income expectation function, n and a2,
are functions of the amount of pesticides, used (X) directly and indirectly,
since the mean loss and loss variance also depend on X.
Consistent with established decision theory, the farmer is assumed to
choose that action (level of pesticide use) that maximizes his expected
utility, which is a function of both the expected net income and the net
income variance — a measure of risk. The expected utility for a given
level of pesticide application can be determined from the parameters of
the net income expectation function through the mean-variance frontier
technique, as described in Halter and Dean [ 10 ].
Consider utility as some function of net income, U(y). This function can
be written in form of a Taylor series expansion as a. function of powers of
(y - c), where c is some constant:
dy
If the arbitrary constant in this expression, c, is set equal to u , the
expected net income for the given level of pesticide use, the Taylor
series expansion becomes:
00 (y - P )
(A. 4) U(y) = I - *-
n=0 nl
•*-
Taking expected values on both sides of the equation yields the expected
utility as a function of the moments of the net income expectation function
and the derivatives of the utility function, evaluated at wy:
*The derivation of the mean and variance of a transformation of a random variable
is described in work statistics textbooks? for example, W.C. Merill and K.A.
Pox, Introduction to Economics Statistics* New York, Wiley, 1970; p. 135.
66
-------
00 E[(y - y )n d(n)U(u
(A.5) E[U(y)] = M nj
n=0 dy
Frequently, only the first three terms in the right-hand side expression
(n = 0, 1, 2) are regarded as significant.
Decision research in agriculture generally is based on the assumption that
farmers exhibit risk-averse behavior. This behavior implies that the
farmer is willing to give up some expected net income for a reduced risk.
A functional form of the utility function that satisfies the assumption
of risk aversion is the logarithmic form:
(A.6) U(y) = In (y + a) ,
where the constant a is introduced to assure the existence of the natural
logarithm; it must be greater than the maximum possible loss (negative
net income).
For this specification, the expected utilities for each level of pesticide
application can be obtained on the basis of Equation (A.5); dropping all
terms in the sum for n > 2, we obtain
a2 d2u(y )
(A. 7) E[U(y)] = U(w ) +
y 2
dy
2
Since both the mean and the variance of the net income expectation function
are dependent upon the level of pesticide application, Equation (A. 7) can
be used directly to determine the expected utility for any given level of
pesticide use. The procedure outlined here has the advantage that no
estimates of the probability densities for individual loss levels are re-
quired. The functional form of the loss expectation p.d.f. therefore does
not have to be specified. Alternative estimates of the two parameters of
this function can be used directly to assess the potential impact of pest
management information programs with a minimum of computational operations.
69
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Unfortunately, this relatively simple technique is incapable of handling
the analysis of the impact of alternative insurance schemes. Only "pure"
coinsurance schemes can be examined by means of the mean-variance frontier;
the coinsurance factor would modify the relationship between percentage
loss and net income described in Equation (A.I). However, as soon as a
deductible is introduced, the loss expectation function changes from a
continuous to a "hybrid" function. Loss expectations over the range of
the deductible are defined by the original loss expectation function; beyond
the deductible, the farmer is certain of his maximum loss (or minimum net
income). Mathematically, this situation can be represented as follows:
D
(A. 8) y - / s f (s) ds + (1 - y) (1 - D) ,
S 0
where D = deductible, defined in terms of the fraction of
crop lost;
D
Y = / f (s) ds, the probability that the actual is less
0
than or equal to the deductible.
This "hybrid" probability density function necessitates the specification
of f (s) , the underlying p.d.f. of the percentage crop loss. The functional
specification used in the simulation is based on the assumption that the
farmer's loss expectations can be described in terms of a positively
skewed p.d.f., i.e. that lower percentage losses are generally more likely
than higher ones. The general r-type p.d.f. satisfies this requirement, as
specified in Hogg and Craig [ 13 ] :
(A.9) f(s) =
where s = percentage of crop lost because of pest damage;
a,$ =» parameters,
T(a) - a constant given by
oo
(A. 10) T(a) » / z"~l e"Z dz.
0
The relationship between the parameters of the r-type p.d.f. and its mean
-------
and variance can be determined from its characteristic function:
i-f-ei
(A. 11) (t) = E[eltS] =
- 3it)a
Differentiating this expression and evaluating it at t=0 yields the mean
and the variance
u = cx3,
(A.12) S
a2 = a|32.
s
The parameters of the loss expectation function can therefore be estimated
on the basis of estimates of the mean and variance of the function.
The numerical estimation of the T-type densities associated with different
levels of loss requires the use of approximation formulae; a direct trans-
lation of Equations (A.9) and (A.10) into computer program statements would
introduce serious inaccuracies. For the densities themselves, the follow-
ing approximation formula (as given in textbooks on numerical analysis) has
been used:
where F(s) is the cumulative probability distribution of the percentage
loss (s) . The F(ot) constant is estimated by means of the expression:
(A.14) F(a) = 1 - .57486 (a-1) + .95123 (a-1)2
- .69985 (a-1)3 + .42455 (a-1)1*
- .10106 ( -I)5
This approximation formula implies an error of less than 5*10 5.
This specification of the mathematical approach still implies one source
of inaccuracies that may influence the computations. F(s) approaches unity,
as s approaches infinity. In the present situation, the evaluation of the
integral of Equation (A. 9) is limited to the interval [0, 1]. For low
expected losses, we have F(l) - 1. For higher expected losses, the inaccuracy
*Both approximation formulae have been taken from M. Abromowitz and I.A.
Stegun, (eds.), Handbook of Mathematical Functions. New York, Dover, 1965.
71
-------
may be substantial; for example, for y = .5, we have F(l) = .865. The
s
probability densities have therefore been adjusted in the simulation pro-
gram to yield more accurate estimates.
72
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APPENDIX B
73
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PECTATION — THRflllQH A CHANGE OF VARIABLE TFCHNlOUEi AS WELi' *
COHHON/EQUA/A(9t7)tBlT)iPl*i>(7)
— GOHHON/OREI/AVY t9t7) »^OY(9f7)-—
COMHON/VIER/AVII(9,7».»VU?(9.7I
— COMUOM/PARA/AL (q) vBt(Q) ?coi *> tO£tT)
DIMENSION SUB(5),PANS(7)
DATA ae/.620,.73H..820,.BVO,.9»0,.,flo,.996,.99i,.980/
DATA CO/1 ,.5,1 , 1 rl ,1 ,1 /
DATA OE/l.,l.,0.,.i,,?,.2b,;*/
DATA SUB/t.t.9t. 751.5,0. /
3 PANS(I)«PINS(I)
Stl)"0-
00 5 I»2.10J
DO 1 IP.1.2
00 1 T'-'F.l,1
00 1 ISUH.1,5
pn i til..
2 PINSII)«PANS(I)»SUB(ISUB)
CALL TT9L
REKIND 2
00 * JM", 9
AX(J)>AL(J)*BE(J)
AS (J) «*L (J> *BE ( J) ••?
CALL QAMRA(AL(J),BO,IER)
WRITE (2)P
4 CONTTMllr
REWIND 2
CALL UTILITY(C.n.INF)
CALL REPORT ( INF.YMINI
1 CONTINUE
REWIND 2
-------
-000106 PRINT 6.(AXtl),7XtII.I«l,9»!(ASU»-,7SIU.I«l.'»
000132 6 FORMAT(•! COMPARISON Of MEANS *ND STANDARD OEVIATIONS>//9|10X
—. aei a .5 *» /»( WXPEW. s/ti
00013Z CALL
ENO-
-------
' SUBROUTINE INCOME(INF,YMTN,IP|
•^» ******************•*•**"*'*»••••••*»»*••«»»•«»••»»«•«•«•• »«!•••»>»»»»>»»«»««>«»-
C* •
C» DIFFERENT LEVELS OF LOSS.
Tgr> net mcoHe LEVCLS FOR
000006 COMMON/ZWEI/YLOSSllOl,
00000
000006 COMMON/EOUA/A(9.7iiB(T)»PlNS(7>
.J00006 COMMON/UNO/"fA " "
000006 YLOMAX*700.
000007
000011 TC>170.»FLOAT|INF.l)*l.S
0000« 06 1 K»l,f
-000023
000026 LlM«lFIX(nEEKKl«l
000030
000032 XLBSBS.orLOATlJ.il
00003*-
000046 B(K)>P*YLOMAX*CO(K)
000052 : 00-3-1*
000054 Y(I.JiK)«A(JlK)-B(K)«s(I)
000074 3-CONTINUE-
BOTTOM
-------
SUBROUTINE UTILITY (UMjlg.O. INF)
—€**•*•»•••••••»••»»*»»•»•«••*•«••»••««••••»•«««••«»••«»**>««•«•*
C»
-C" *HIS-5UBROUTINE-COMPUTES THE OTtflTlES «S59ct*TEP MtTH BlFfrRENT •-
C* NET INCOME LEVELS. JHE UTILITY FUNCTION IS GIVEN BY THE •
-C« N*TUHAU-L06»BiTHM Of NCT 1NCOHC, aTANPiPDIZtO-SUOr-THAT U M»X- 100 »-
C* AND U HIN • 0. •
-GOHMOU/E-JN
000006 F*CTOB«1.
OOOOOf 00-l-K«lt7-
000011 DO 1 Jal.9
000018-
000013 U(IiJiK).F4CTOP»ALOO(Y(I.J.K))
-CCNTWUE-
000040 • IFIINF.6T.1IQO TO 10
00004»-
000044• UM*X>I»1.)*UMIN
000.0
OOO.Q4T 00 II J«lt9
J,K»
000117 2 CONTINUE
-000125 D«.(UMAX-UMUW
00012T RETURN
-------
SUBROUTINE PROB*B(CtD,YMtN»
C*
C»
c«
THE BASIS OF A LOSS EXPECTATION FUNCTION OEPINED RV THE GAMuA-
OISTRiauTlONi--THg SUBROUTINt-CnxPUTES-fXpecTEtrVriMT-IlfS-FtRST
THROUSH A TAYLOR SERIES txpANSion or THE UTILITY FUNCTIONI THEN
C»
000006
000006
000006
000006
• •" 000006
000006
000006
000007
nnnnn
000016
00001T
000027
— 000031
000032
• 000035
0000*2
000046
000055
000057
COWMON/D6 - .
10 PRINT ll.J.K
U FORMAT l*nSTANOARD OEVTATION IMAGINlOV , rOB..*CTlnu*l2«. Pnl Irv»Til , . — .
000207
SDY(J«K)»0«
000231
-0002*2-
0002*6
-0002*5-
0002*7
*VUtJiK>»»VU(J,K)-SDY
-------
000300 BS»»8S)
-000313 CHU»CHU«OR»BS
-------
CO
o
SUBROUTINE KEPORT (INF.YMIN)
000005
000005
000005
0000-W —
000010'
000013
000014" •
000024
01)0033
00003T
000041 —
000045
0000*7
000053
OOO1)"?
000057
omsT
000070
000070
000111
oonin
000115
000115
000126
000147
000153
000164
000205-
000211
000211-
• 000211
nnnsn
000211
T00215
0002*7
nnnacn
C«
».
11
11
14
10
2
3
4
5
31
2.1
22
COMMON/ORtI/AVYt9,M»SOY(9, )
PRINT 1
-FORMAT (lHt/10X*CL)MMARY RrPflflT ON Tuv rvrrrTfT Or Ai TrnutTTUr TiijIIDA
.NCE SCHEMES. */10X«-- LOSS EXPECTATIONS! INFORMED. •//)
00 15 J-1.9 .
00 TO(11.12tl3)INF
PRINT 21
00 TO 14
PRINT £H
00 TO 14
PRINT 23
CONTINUE
00 I NT 10
FORMAT(///10X»1. EXPECTED NET INCOMES**//)
••PRINT • Zt 11 1 !•)' .9) •
FORMAT! IX*— > ACTION*/ *X»— •5X.o(6«T2<5X>/ 1X*POLICY — •/)
FORMAT! 3XIl«8X«(El?.S>lX»
PRINT 4<.
FORMAT! /// 1X*2. EXPECTED UTILITIES |H.V APPROACH).*//)
-PRINT 2r!l»l*l.Q)
PRINT 3. (J,(AVU(l,J)it«l,9).J«l.f)
-PRINT -5
FORMAT! /// 1X*3. EXPECTED UTIUITjFS IC«0-V AppROACH) .*//)
_PR{NT 2».(t-t I«lt9)
PRINTS. IJt (AVU8(I,J) f T«l,9) .J.l.r)
FORMAT!////)
FORMAT I1H09X*! INFORMATION- SERVICtS-FULL-V--SU8^IOI7ED )•) •
FORMAT I1H09X*| INFORMATION SERVICbS sV~PER CENT SUBSIDY.)*)
FORMAT !1H09XJI.! INFORMATION SEDVICtS RQOvIOED AT rULL COST )*)
PRINT 38
>. FORMAT !X//10X*4V STANnARO-OCvIATIOM"!*//)
PRINT 2.(I.I«1.9)
-PRINT 3i (Ki (SOY( JIK| T J-l i°t •<-!• ')
RETURN •
-------
SUBROUTINE (JAHRA (XX.OX. 1ER>
• • •«•• x««>**«»^»**<^»M>^»
C«
-C« THIS-SUBROUTINE CALCULATES'THE vaLUf or THE aAHHAnCONSTAMT
C»
000006 IF(XX-57.)6i6,4
000011
000013
000014 •
000015
000016 •«
000017
natinpa
000025
000030
000034
000048
000052
000055
000056
000061
HAAAA-t
GX.1.E75
RETURN
6 X«XX
IER«0
IF(X-Z.)S0.51,15
IS X»X-1.
00 TO 10
63 Y~fLOAT ( |NT (?tj ) ^)t
TO ir(X-l.)80|80,UO
X«X«1
110 Y«X-1.
CYal .*<«<-. 5T7jnl7(.^,p i a » v« 1 . na»aa4-»*¥*^^-s*»*Ta:
.9«Y«I,25»a205*Y«|..«Sl 4993)))))»
JDOXOJ ox=ox»av
000103 120 RETURN
flflm A4 I 3A fFDal
000105 RETURN
04U46 END
00
-------
SUBROUTINE GAMZA(POii.B,jA.AXtASI
-6•*•••••••*••«•••••••••*«•••»••••»»••»••»»*«•**«****«>*»i
C*
c«
FOR GIVEN VALUES OF ALPHA AND BrTA.
GO
to
c»
000911
000011
000011
000011
000013 -••
000015
000016
000021
000024
000025
000031
00003%
000042
000013
000045
nnnnej,
000055
000057
000064
000967
000072
000075
000106
000107
000111
OfHKVlT
•-
COHMON/OUE'NFACT C«5)
ASiAX.O.
CHK.O.
SUaO.
5InS(t)/0
DO 2 K«1,J5
KEPaK-1
- KUPvHOD(KEPtZ)
IF(KUP.NE.OIKAPm-l
JFIH.EO.OIGO TO 30
00 TO 40
40 BUR>KAP»SI6NA/( (A»NI*NFACT(K) )
2 CONTINUE
SVcSU»B»*
BUaSU
AXn»X.S(I)»P(I)
1 CONTINUE
RETURN
6W-- ; ' , ,
-------
SUBROUTINE FCTRL
c»
-c» THts-sufl'iouTt*E-CAb€UbATE5 THh cteTpRiAus neauinco IN Tne-
C» APPROXIMATION FORMULA FnR THE OA«MA.FUNCTIOu. .
000002 NFACT(J)»NFACT(2)«
-00-l-KaTT>S-
000006 ) NF4Cni)«NFACT(I-l)»(I-ll
-»0**15 RETURN
000016 END
CD
U)
-------
000003—
000003
• -000003 -
000003
— 000003
000003
000005
000012
000023
—000025
000026
0000-34
000044
000047
000051
— 000054—
000056
000060
000061
SUBROUTINE ADJCY«1N|
C» PROBAB TO MODIFY THE PROBABlUITlFS. ' •
COMHON/EOUA/A(<),7>iB(T)iPINSl7)
COMMON/QU»TKO/AI>Mt9),AD5(»l
00 1 J«l,9
YHwft'i Jf 1 J *8 ( 1 ) *A« ( v) **YHlN
YZM«YZS«0.
YZH«YZM.Z(I>»Y(l,Jfl)
YS»YS*YM»*a
AD" I J) »Y3/Y1S
4 AOM(J)«YN/Y£H
REWIND 2
END
00
-------
Co
SUMMARY REPOPT (
»
)N THE EFFECTS
rjONS1-iNF«RH(
, OF ALTERNATIVE INSURANCE SCHEMES.
•Of
*
1 i CKPCCTCO NET INCQMFE i
— ACTION
POLICY —
1
3
5
A
7
3.583HOE+00 3.03720E+01
-5»60lBlE*00 ?»?7A*.oe*ni
4.10QOOE*01
1.64B74E»01
1.41S36E*01
3«70000E*01
-2-.059B2F-OJ —
2>14573E*Ol
2.666S9E»01
S.U880E*U1
3.57182E-*Ut
3.Jnoooe»oi
2.54489E*0]
3.70'02E*01
6.70992E«Oi 7,7155?E«01 o.45l20E«01 B.4flB4SE»01 8.0B84SE«01
— -4r47850E*0) — 5,00644E-»01 — ct350BOf*01 — 5.?357BE»OJ — 4.8301
9.20300E«01 9.19979E*01
9.1«fc21E.01 9.23876£«01
9.20470E«01
9.30B20E«01
a
9
4
.S5A62£-»-0 1_
,3B337E«Ol
9.?0902E«Ol
«,?8047E-iOv-
9.36343t.O)
?
_9»6esa2Eta4_
9.20SS7E»OJ
— Qr3A4] OE^fH —
9.3g704E«01
6
_»..t7a*7EJjXl-
o.52490F«01
o.i9fli;c*oi
_9
9
-9
9
—9
9
—9
7
.52523E+01
,1761SE»01
.3t3*4E»01—
.42034E*nl
,52-39*8**!—
8
-9-.763»lE««.l-
9.48926E«01
9.13460E*01
9.27439E*Ol
9.3B?85E»01
^,48(IOSE»01-
9
« tt ttf")
9.4149lE»01
9.07114E«OI
9.3050ftE*01
-UTILITIES (C-Q*V APPROACH)!
7.96523E»01
B.086S8EfOJ
9.436]9E*01
9.18748E»01
9.12T21E»01
8.55»77E»01 9.03*63E»U1
8 .S7297EJ.OJ B.9A»aOt>J).l
•39n82E«01 9.JA084E*0]
•23S77E«01
.29005E»01 —
•25370E»01
9.28094E«U1
9^3<>-t44EA04
4
— 9
«
.-<7732E«Ol
.32221E.01
-«&l%1FA.Ot._
9.31548E.01
— »ra»«81E*»J-
9.444S8E«Ol
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
4. Title
Crop Insurance and Information Services to Control
Use of Pesticides
/. Authors) John A> Miranowski, Ulrich F. W. Ernst,
Francis H. Cummings
9. Organization
AST Associates Inc
55 Wheeler Street
15. Supplementary Notes
10. Project No.
1BA030
//. Contract/Grant No.
68-0
Environmental Protection Agency Report
Number EPA-600/5-74-018, September 1974
is. Abstract This study analyzes the relative effectiveness and
efficiency of pest information and crop insurance programs in encouraging
farmers to use potentially harmful pesticides more sparingly by eliminat-
ing wasteful applications. Possibly excessive applications of pesticides
can be attributed to poor timing of applications and to the risk-averse
behavior of farmers. Focusing on insecticide use in cotton production as
a major policy problem, the study employs a decision-theoretic framework
to simulate the farmer's pesticide use decisions under alternative
program options and subsidy levels. To the extent possible, empirical
data are analyzed to complement the findings of the simulation analysis.
The theoretical and empirical analysis in this study indicate that
pest information programs are potentially more effective than crop
insurance programs in reducing insecticide usage. These reductions from
compliance with pest control recommendations provided by information
programs are associated with economic gains by the farmer. Both the simu
lation experiments and available evaluations of the USDA Pest Management
Program indicate that a maximum insecticide use reduction of 30 percent
can be achieved through information programs. Subsidies to such programs
appear an effective means to encourage adoption by farmers, at least in
the initial phases.
17a. Descriptors
*Pesticides, *Crop Insurance, *Information Services, Scout Programs,
Insecticides, Cotton Production, USDA Pest Management Program, Federal
Crop Insurance Corporation
17b. Identifiers
*Pest Control, Implementation Strategies
17c. COWRR Field & Group
18. Availability
6PO
Abstractor
Send To:
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 2O24O
WRS1C 1O2 (REV JUNE 1971)
------- |