Risk-Efficiency Analysis of the Uee
of: insecticide to Control Vei~e
Bean Caterpillar for SoYbeans
in North Florida
TABLE OF CONTENTS
LIST OF FIGURES ................................ ii
LIST OF TABLES ................ ............... iii
ABSTRACT .................. ........ ......... iv
INTRODUCTION .................... ...... ........ 1
ECONOMIC CONCEPTS OF FARM RISK ................... 2
Risk in Utility Theory.................... ........ 2
The Theory of Stochastic Dominance and Risk Efficiency ......... 5
PROCEDURES ..................... ............ 7
RESU LTS . . . . . . . . . 9
CONCLUSIONS ................. ............ 12
REFERENCES ........... ... ................... 14
LIST OF FIGURES
Figure 1. Diagramatic Representation of Risk Aversion and The Cost of Risk 4
LIST OF TABLES
Table 1. Definition of Groups of Farmers According to the Lower and Upper
Bounds of Their Absolute Risk-Aversion Coefficient . . 9
Table 2. Mean, Coefficient of Variation of Income and Probability of Negative Net
Income for Different Economic Thresholds of Velvet Bean Caterpillar
(VBC) Insects on Soybean for a 100 Acre Farm in North Florida... 11
Table 3. Average Number of Applications of Insecticide for Velvet Bean Caterpillar
Control on Soybeans... ........................ 11
Table 4. Risk-Efficient Set of Economic Threshold Levels for Spraying Against
Velvet Bean Caterpillar (VBC) Insects on Soybeans for Different Groups
of Farmers Classified by Their Risk Attitudes.. . . .. 12
Cumulative probability distributions of income are derived for a 100 acre non-irrigated
model soybean enterprise in North Florida. The distributions are obtained by establishing
several economic threshold levels through scouting at which spraying velvet bean caterpillar
(VBC) is carried out.
The income distributions are subjected to stochastic dominance analysis to determine
efficient threshold levels for different groups of farmers classified according to their risk
attitudes. The results indicate that setting the threshold level at a sample average of four
medium and large VBC larvae per of three-foot section of plants in a row yields the highest
income and is also the most preferred threshold for all risk-averse individuals.
Key words: pest management, risk, soybeans, stochastic dominance, uncertainty.
RISK-EFFICIENCY ANALYSIS OF THE USE OF
INSECTICIDE TO CONTROL VELVET BEAN CATERPILLAR
FOR SOYBEANS IN NORTH FLORIDA
Kwabena A. Anaman, James W. Jones and William G. Boggess
Velvet bean caterpillar insect is one of the major soybean pests in North Florida. Left
uncontrolled, it can cause serious economic losses to the farmer. Soybean is one of the
important crops in the North Florida an area where agriculture is the major key industry.
Income instability of farmers in the area has been particularly severe in the 1980's. The
major causes of instability include production risks caused by droughts and pests damage of
crops (Boggess et al, 1985). Reducing the instability, and hopefully increasing mean farm
incomes, requires strategies to control production risks. A typical strategy is the elimination
or reduction of economic losses of crops through pest control.
Control of crop pests has been achieved either by conventional or integrated pest
management strategies. Conventional pest management involves setting routine dates for the
application of insecticides without regard to the fluctuations in the population of the pests.
This strategy usually leads to higher use of pesticides than integrated pest management
strategies and possibly greater ecological spillover effects. To alleviate the latter problem,
integrated pest management strategies have become increasingly used in recent years.
Integrated pest management deals not only with the management of the pests but also the
effect of the methods employed on the host (the plant) and the environment.
*Former Graduate Assistant, Department of Food and Resource Economics, Professor,
Department of Agricultural Engineering, and Associate Professor, Department of Food and
Resource Economics, all at the University of Florida, Gainesville, FL 32611.
A common integrated pest management strategy is scouting which is widely used in North
Florida. Scouting involves periodically sampling soybean fields to determine whether a
decision to spray should be undertaken. Spraying is then carried out if the pest population is
above a certain critical level following recommendation by the Extension Service.
Feder (1979) has emphasized that pest control decisions are generally risky. Because of
the risky nature of pest control decisions, Greene et al (1985), have argued that any
evaluation of integrated pest management strategies must consider entire probability
distributions of net returns rather than using only the first and second moments (eg. mean
and variance). The risky nature of pest management control strategies means that different
groups of farmers may use different levels of the control measures because of their
perceptions and attitudes towards risk. A fixed recommended level of application for all
farmers may not meet individual farmer's objectives. Hence, the commonly recommended
economic threshold levels have to be evaluated using procedures that can handle cumulative
probability distributions of income. The objective of this study, therefore, is to evaluate the
risk-efficiency of the economic threshold for the use of insecticide to control velvet bean
caterpillar for soybeans. The evaluation is being done to determine the optimal threshold
level for different groups of farmers classified by their risk attitudes.
ECONOMIC CONCEPTS OF FARM RISK
Risk in Utility Theory
The most widely used theoretical framework to evaluate economic decisions under risk
and uncertainty is utility theory. Utility theory states that a utility function exists for a
decision maker whose preferences are consistent with the axioms of ordering and transitivity,
continuity and independence. The utility function associates a single real value with any risky
project. The individual will always choose the project that yields the highest mathematical
expectation of the utility function of some outcome. The outcomes of the utility function
could be income or wealth or time streams of consumption. The mathematical expections are
based on the subjective probabilities of outcomes.
If the individual is risk averse which is the widely accepted norm of behavior for most
farmers, then his or her utility of income increases at a decreasing rate as shown in Figt. 1.
Figure 1 shows two possible outcomes Y1 and Y2 resulting from two states of nature if a
particular project or farm plan (A) is selected.
The expected monetary value (EV) of any farm plan or project is the mean of the
outcomes of the project. Hence, the EV is just the sum of the product of the income and
probabilities for each possible outcome. The certainty equivalent (CE) is the level of income
which if received with certainty yields the same level of utility as the uncertain project
(EU(A)). If the decision maker is risk averse, the CE will always be less than the EV. The
difference between the expected value and the certainty equivalent is termed the cost of risk.
The cost of risk has been determined to be a function of income by Pratt (1964) as follows
for small risks:
C = -U"(Y) var (Y)
where C is the cost of risk, U" is the second derivative of U(Y), U' is the first derivative of
U(Y) and var (Y) is the variance of income.
The cost of risk is the basis for the producer's willingness to accept a reduction in
expected income in return for a reduction in variability or risk. It is directly proportional to
the variance of income indicating that a farm plan with higher variance entails a higher cost
of risk. It is also a direct function of (-U"/U'), which is termed the absolute risk-aversion
The absolute risk-aversion coefficient is an individual characteristic and therefore varies
from one individual to another. It may depend on such socioeconomic characteristics as the
level of experience in farming, size of the farm, the types of agricultural commodities
1 i '
I J -
c I ,\
Y CE EV ,
1 C 2 Income
Figure 1. Diagramatic Representation of Risk Aversion
and the Cost of Risk.
produced, financial status of the farmer, educational level and the reliability and strength of
the technical support system behind the farmer.
The concept of the absolute risk-aversion coefficient derived from utility theory is a key
tool used in risk-efficiency analysis involving stochastic dominance methodology. The
stochastic dominance methodology is discussed below.
The Theory of Stochastic Dominance and Risk Efficiency
Stochastic dominance methodology is an efficiency criterion used to order or rank
choices for a particular group of decision makers. It divides the decision alternatives into
two mutually exclusive sets: an efficient set and an inefficient set. The efficient set contains
the preferred choice of every decision maker whose preferences are consistent with the
restrictions imposed by the criterion. Inefficient alternatives are not considered because no
element in the inefficient set is preferred by any of the members in the group.
Given any two probability distributions of income f(y) and g(y) defined over the relevant
range (a-r) and defining cumulative probability distributions FI (Y) and G1 (Y) as follows:
FI (Y) = a r f(y) dy; GI (Y) = a r g(y) dy
then farm plan F is stochastically more efficient than farm plan G if FI(Y) < GI(Y) for all
possible r. This type of stochastic efficiency is termed first degree stochastic dominance.
First degree stochastic dominance of f(y) over g(y) establishes only that f(y) is preferred over
g(y) by the farmer whose marginal utility for income is positive or, in other words, prefers
more income to less.
Second degree stochastic dominance (SSD) rule provides a more powerful tool to evaluate
different farm plans and management strategies. The rationale behind the SSD rule is that
the farmer has both a positive and a diminishing marginal utility for income, illustrating risk
aversion. The SSD rule can also be stated in terms of the cumulative probability functions.
The distributions Fi(Y) and GI(Y) are defined as follows:
F2(Y) =a f r F1(Y) dy; G2(Y) a f r Gl(Y) dy
If F2(Y) 5 G2(Y) for all possible r, then farm plan F is more risk efficient than farm plan G.
Meyer (1977) has generalized the stochastic dominance theories in such a way that the
first and second degree stochastic dominance rules become special cases. The generalization is
called the stochastic dominance with respect to a function or generalized stochastic
dominance. Under this technique, classes of decision makers are defined by specifying lower
and upper bounds on their absolute risk-aversion coefficient (A(Y)). The absolute
risk-aversion coefficient is defined as
A(Y) = -u"(y)
where u"(y) and u'(y) are the second and first derivatives of the utility function of income
u(y). The level of absolute risk aversion coefficient indicates whether the farmer is risk
averse or risk loving. A negative value implies risk-loving behavior while a positive value
indicates risk aversion. A value of zero implies risk-neutral behavior which is identical to 'i,
maximization of expected profits.
The lower and upper bounds on the farmer's absolute risk-aversion coefficient AI(Y) and
A2(Y) define an interval measurement of his or her preferences. Second degree stochastic
dominance implies that AI(Y) = 0 and A2(Y) = oo. First degree stochastic dominance then
means that AI(Y) = -oo and A2(Y) = oo. Specification and elicitation of the absolute
risk-aversion coefficient intervals can be done by procedures developed by King and Robison
(1981). Meyer (1977) describes in detail the mathematical procedures used to rank strategies
with the stochastic dominance with respect to a function methodology.
The soybean integrated crop management (SICM) model is used in this study to derive
yields and net income. This physical crop simulation model is the result of work done by an
interdisciplinary research development team at the University of Florida, Gainesville, Florida
involving entomologists, agronomists, agricultural engineers and economists (Wilkerson et al,
The model components include crop, soil, insect (velvet bean caterpillar), tactics
(pesticide and irrigation applications). The model is designed to allow the user to study
soybean pest control and irrigation management at the field level under different weather, soil
and insect scenarios. The model has been validated using actual field data from Quincy and
Gainesville in North Florida.
The simulation model is used in this particular study to calculate yield and net income
for various pest management strategies. A 100 acre soybean crop enterprise is assumed
representative of North Florida farms (Anaman, 1985). Hence, the net income of the
enterprise is derived by converting the per acre results from the model to the 100 acre farm.
The costs and prices used for the study are for the 1982 production year (i.e., soybean price
of $7.00/bu., scouting costs of $5.00/acre, insecticide application costs of
$3.00/acre/application, Lannate price of $13.25/lb. of active ingredient and other variable costs
Pest management simulations are considered for the farmer assuming certain fixed
production conditions. These conditions are no irrigation, average planting date, average row
spacing, average plant spacing and the use of lannate insecticide to control the velvet bean
caterpillar applied at a rate of 0.6 pint per acre per application.
When the caterpillars are smaller than 1/2 inch long, beneficial organisms may be able to
kill most of them and they inflict little damage. However, when they are 1/2 inch or longer,
they can do a lot of damage. Hence, control decisions are based on medium and large larvae
populations (those 1/2 inch or longer) (Northrop and Koehler, 1984, pp. 22-23).
The farmer modeled is deciding on the economic threshold level at which a decision to
apply the insecticide will be made. The threshold level depends on the sample average number
of medium and large VBC larvae per three feet section of plants along a row determined i.: ..
scouting. There are seven possible threshold levels for this study: 2, 4, 8, 12, 16, 20 and
The farmer's decision to apply the insecticide at a given threshold level is risky because
of the several sources of risk. These sources are the weather variability, the degree of influx
of the insects and the time of first arrival of the insects. Thui the economic losses due to
insect damage and economic benefits from spraying are unknown to the farmer at the
time the decision to spray has to be made.
This study allows for three degrees of influx level small, average and large and three
possible times of first arrival of the insects early, on time and late, giving nine possible
combinations (Wilkerson et al, 1983). The tenth one is the case of no insects appr':.'
during the growing season. Ten years of actual rainfall data, 1954-1959 and 1978-1981 are
randomly selected and used to derive the non-irrigated yields of the crop using the 5'. ..,'
Model. Hence, there are 10 insects and 10 weather possibilities, making a total of 100
combinations for which net income are derived for each economic threshold level. The
cumulative probability distributions of income for the different threshold levels are subjected
to the stochastic dominance with respect to a function analysis to determine the efficient
threshold levels based on the risk attitudes of the different groups of farmers.
The key input needed to use the stochastic dominance with respect to a function
methodology is the absolute risk-aversion coefficient intervals of the target farmers, in this
case North Florida soybean farmers. Since no empirical work has been done to estimate
farmers' utility functions and hence the absolute risk-aversion coefficient in Florida, secondary
work from other areas of the United States are used to establish the intervals (Kramer and
Pope, 1981; Wilson and Eidman, 1983; King and Oamek, 1983; Rister et al, 1984; and Love and
Robison, 1984). Table 1 lists the various groups of farmers defined by the lower and upper
bound of the absolute risk-aversion coefficient. The absolute risk-aversion coefficient
intervals chosen are those that are common to all of these studies.
The proposition tested is that farmers should behave differently in their choice of the
economic threshold levels to apply insecticide to control the velvet bean caterpillar according
to their risk attitudes.
Table 1. Definition of Groups of Farmers According to the Lower and Upper Bounds of Their
Absolute Risk-Aversion Coefficient
Absolute Risk-Aversion Coefficient
Type or Group of Farmers Lower Bound Upper Bound
Risk Loving -0.00050 0.00000
Very Low Risk Averse 0.00000 0.00003
Low Risk Averse 0.00003 0.00010
Moderate Risk Averse 0.00010 0.00050
High Risk Averse 0.00050 0.00100
Table 2 reports the mean, standard deviation and the coefficient of variation of income
for the different economic thresholds. Threshold 4 yields the highest mean income and also
the lowest coefficient of variation of income. Not surprisingly then, it has the lowest
probability of negative net income (that of 0.26). The mean income peaks at Threshold 4 and
falls gradually with increasing size of the threshold.
The average number of applications of insecticide against the caterpillar for each
threshold level is presented in Table 3. These results indicate that the average number of
applications declines with increasing level of threshold. Threshold 4 which yields the
maximum profit results in an average of approximately two applications of the insecticide
during the growing season.
Table 4 shows the risk-efficient set of threshold levels for the different y:ouri of
farmers. It can be observed that Threshold level 4 dominates all the other threshold levels
for all groups of farmers, both risk averse and risk loving. Thus, the proposition that farmers
should behave differently in their choice of the level of economic threshold at which to apply
insecticide is rejected. All farmers whether risk averse or risk loving should find the
threshold level of four VBC larvae per sample, the optimal choice under the conditions of the
Table 2. Mean, Coefficient of Variation of Income and Probability of Negative Net Income
for Different Economic Thresholds of Velvet Bean Caterpillar (VBC) Insects on
Soybean for a 100 Acre Farm in North Florida.
Mean Net Coefficient Probability of
Income in of Negative Net
Threshold Levela Dollarsb Variation Income
2 5898 1.24 0.28
4 5976 1.23 0.26
8 5633 1.31 0.27
12 5235 1.42 0.30
16 4849 1.54 0.31
20 4565 1.67 0.32
24 4268 1.81 0.32
a Sample average number of medium plus large VBC larvae per three-row feet.
b Income calculations are based on 1982 price and cost conditions.
Table 3. Average Number of Applications of Insecticide for Velvet Bean Caterpillar Control
Average Number of
Per Year Over the
Per Year Recorded
2 2.70 5
4 1.98 5
8 1.29 3
12 0.88 2
16 0.73 2
20 0.55 2
24 0.36 2
a Sample average number of medium plus large VBC larvae per three-row feet.
b An application consists of 0.6 pint of Lannate per acre.
Table 4. Risk-Efficient Set of Economic Threshold Levels for Spraying Against Velvet Bean
Caterpillar (VBC) Insects on Soybeans for Different Groups of Farmers Classified by
Their Risk Attitudes.
Type or Group Efficient Set of
of Farmers Threshold Levelsa
Risk Loving 4
Very Low Risk Averse 4
Low Risk Averse 4
Moderate Risk Averse 4
High Risk Averse 4
aSample average number of medium plus large VBC larvae per three-row feet.
This study has analyzed the risk efficiency of various economic thresholds for spraying
velvet bean caterpillar (VBC) on soybean and concluded that the threshold level of four VBC
larvae per sample is the preferred strategy for risk-averse farmers. Fixed soybean price (i.e.,
$7.00 per bushel) and cost of insecticide (i.e., $13.25 per pound at active ingredient) were
assumed using average 1982 production year figures. A procedure such as the one presented
in this report, is needed to reevaluate economic thresholds as prices and costs change as have
happened during the last five years. Since 1982, soybean prices have generally declined while
the cost of insecticide has risen, suggesting that the optimal threshold has increased.
Therefore, it is important to analyse the effects of such changes in the economic environment
on the profitability and risk of production for soybean farmers.
This study focused on the evaluation of the alternative thresholds under non-irrigated
conditions. It needs to be expanded to include irrigated conditions and different types of
insecticide, in addition to lannate. A flexible economic threshold level that changes with the
stage of growth of soybean may be superior to the fixed value used.
Soybeans are more sensitive to insect damage during the post bloom-early pod fill period
than at earlier or later times. The low threshold value of four medium plus large VBC larvae
per sample determined a optimal in this study may reflect the need to control the larvae
during this period. The value of four, may also reflect the observed potential for very rapid
population build-up in the field and subsequent rapid crop destruction. Given these factors, a
flexible economic threshold level that changes with the stage of growth of soybean may be
superior to a fixed threshold.
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