Use of the economic threshold to improve the efficiency of preemergent-herbicide treatment decisions is limited by a lack of weed information. An economic model for assessing the expected value of weed information needed to implement a threshold decision rule is developed. Empirical results suggest that early season weed information can have value in cabbage weed management in Massachusetts.Crop Production/Industries,

Allen, P. Geoffrey

Bhowmik, Prasanta C.

Gillmeister, William J.

Moffitt, L. Joe

English

Research Papers in Economics

Information Value in Weed Management
William J. Gillmeister, L. Joe Moffitt, Prasanta C. Bhowmik, and
P. Geoffrey Allen
Use of the economic threshold to improve the efficiency of preemergent-herbicidetreatment
decisions is limited by a lack of weed information. An economic model for assessing the
expected value of weed information needed to implement a threshold decision rule is
developed. Empirical results suggest that early season weed information can have value in
cabbage weed management in Massachusetts
The value of agricultural yield losses due to weed
pests in the United States each year is generally
thought to be large, perhaps an amount in the bil-
lions of dollars. Farmers also spend a considerable
amount of money to control weeds, Environmental
and health safety costs related to weed-control ac-
tivities, particularly costs resulting from ground-
watercontaminationby herbicides, are also receiving
considerable attention and may be substantial
(Nielsen and Lee).
Several studies have focused on the development
of decision frameworks, usually involving the con-
cept of the economic threshold, to promote more
efficient postemergent-herbicide use in weed con-
trol (e.g., Marra and Carlson; Marra, Gould, and
Porter). Much less attention has been given to pre-
emergent herbicidal weed-control decisions, per-
haps because key information needed to implement
threshold-type decision rules is ordinarily unavail-
able for preemergent treatment decisions. For ex-
ample, use of a threshold requires a measure of the
pest population for implementation. Such a mea-
sure is typically unavailable in the preemergent
case though there is apparently potential for and
interest in its development among weed scientists
(King, Lybecker, Schweizer, and Zimdahl).
A purpose of this paper is to present a method
for assessing the expected value of pest information
William J, Gillmeister is an agricultural economist, Pest Control and
Regulation Section, Resource and Technology Division, Economic Re-
search Service, U.S. Department of Agriculture, Washington, DC;
L. Jne Moffitt and P. Geoffrey Allen are associate professor and pro-
fessnr, respectively, Department nf Agricultural and Resource Econom-
ics, and Prasanta C. Bhowmik is an associate prnfessor, Department nf
Plant and Soil Sciences, all at the University nf Massachusetts at Am-
herst. Funding was provided by the National Pesticide Impact Assess-
ment Program Contract Nos. USDA-TPS U-2057-258 and -259, The
Massachusetts Agricultural Experiment Statinn is gratefully acknowl-
edged.
in preemergent herbicidal weed control. The method
involves estimating information value conditional
on optimal information utilization in the threshold
decision-making context, Value estimates based on
the method shed light on the magnitude of expen-
ditures that could profitably be made by farmers to
acquire such information. Estimates may also pro-
vide basic information for use by research and ex-
tension program administrators in establishing the
priority that might be attached to development of
pest-information models for preemergent use.
The first section discusses the use of information
in preemergent weed management and elaborates
on its valuation. Next, a model for calculating the
expected value of information and empirical results
for cabbage weed management in Massachusetts
are presented. Concluding remarks are given in the
final section.
Conceptual Framework
Preemergent treatments with herbicide are typically
made assuming, at least implicitly, that the weed
problem during the growing season will have suf-
ficiently serious economic consequences to warrant
control. If this assumption turns out to be incorrect,
then a pest-control expense and a potential risk to
environmental resources are incurred unnecessar-
ily. A possible improvement over such a‘’ schedule
spray” use of preemergent material may be based
on utilization of pest information and implemen-
tation of a threshold-type decision rule.
To use a threshold decision rule, information on
the weed population is needed to compare to the
threshold population; however, for a preemergent
application of herbicide, a weed population does
not exist and cannot be monitored in a straightfor-
ward manner at the time the treatment decision
must be made. To circumvent this dilemma re-Gillmeis~er, Mofftt, Bhowmik, and Allen Information Value in Weed Management 25
quires development of some type of weed-predic-
tion model based on start-of-season information.
Such a weed predictor might depend on a number
of factors including weather forecasts, viable weed
seeds in the seed bank, cropping history, herbicidal
control history, and previous seasons’weed weights.
At present, there is apparentlya considerableamount
of interest among weed scientists in improving the
efficiencyof preemergent-herbicideuse and, in fact,
some efforts are underway to develop early season
forecasting tools for weed pests (King et al.), An
interesting related economic issue is the potential
value that might be expected to accrue to devel-
opment of such pest-information models.
To shed light on the value that pest information
might have for preemergent herbicidal treatment de-
cisionsrequites assessmentof the change in expected
profitresultingfrom optimalutilization, in athreshold
decision-making context, of perfect information
(Moffitt,Famswodh, Zavaleta,andKogan).The value
estimate obtained in this manner is therefore inter-
preted as a potential value: It is an upper bound on
the value that early season weed information might
have for preemergent herbicidal treatment decisions
and will differ from actual value to the extent that
sample rather than perfect information and risk aver-
sion rather than risk neutrality prevail. An upper-
bound value estimate, as provided by the method
developed in the next section, provides basic infor-
mation for use in determining the appropriatenessof
committing resources to improving decision-making
efficiency in preemergent weed control.
The Model
Consider the following crop-weed pest model:
(1) fI=pyY-vh -f,
(2) Y = Yo – all”,
(3) W = W. exp (-~h),
(4) w, - A@, 7),
where II is profit, py is cabbage price ($/kg), Y is
yield (kg/ha), v is herbicide price ($/kg ai), h is
herbicide dose (kg ai/ha), $ is fixed herbicide ap-
plication cost ($/ha), Wis the controlled weed pop-
ulation (kg/ha), Y. is the potential yield with all
other inputs fixed except weed population (kg/ha),
a is the unit effect of weeds on yield (kg/ha), W.
is the uncontrolled weed population (kg/ha) with
expected value P and variance #, and ~ is a kill-
efficiency parameter of herbicide.
The model, equations (1)–(4), depicts profit re-
sulting from weed management in a crop-pest sys-
tem characterized by linear pest damage and an
exponential relationship between the weed popu-
lation and preemergent herbicidal control. Com-
mon functional forms and stochastic specification
are employed as useful simplifications of perhaps
more complicated relationships to facilitate ana-
lytical tractability. After estimating parameters, ex-
pected profit can be calculated for a “schedule
spray” strategy in which a preemergent-herbicide
treatment is made routinely at a recommended rate,
h’, and no other weed control is employed. Ex-
pected profit for a threshold-type weed-control
strategy can also be evaluated.
Denote a population threshold by W~, and the
preemergent-herbicide control level by h~. Follow-
ing Moffitt, Hall, and Osteen, expected profit is
given by
(5) E[rI] = , Yo@[(WT – WYUI
/ + p, a [(d 2n) exp(( – l/(2u2)) (WT – 1.L)2)
– ~ @ ((WT – I.L)/u)] + (Py Yo – v~T – f)
. [1 – @((WT – I.L)/u)] – py a exp
(- (3M{(uWZi)exp(( – M2u2))(WT
– p)z)+ p[l – @ ((WT – I’JJYU)I},
where @ is the standard normal cumulative prob-
ability distribution (see Appendix). Expected profit
corresponding to the “schedule spray” manage-
ment strategy at a recommended rate follows from
evaluation of (5) with h~ = h’. Equation (5) can
also be used to calculate the expected profit for a
threshold-type strategy in conjunction with early
season weed information.
Threshold-type strategies have been particularly
popular in pest-management decisions. Maximi-
zation of (5) with respect to WT and h~ results in
the largest expected profit among management
strategies of the type: If a population threshold is
exceeded, then apply a preemergent-herbicide
treatment at the rate hi-; otherwise do not use pre-
emergent control. Necessary derivations for the op-
timal threshold and level of control associated with
(5) are considered in an empirical example in the
next section, Given the optimal strategy, expected
profit can be evaluated and used to obtain the value
of weed information corresponding to information
use in a threshold-type strategy. Results indicate
the expected value of early season weed informa-
tion and provide an upper bound on maximum will-
ingness to pay when information is utilized in the
context of a threshold decision strategy.
Value of Cabbage Weed Information in
Massachusetts
Weed pests, mainly grasses such as crab grass and
fall panicum, and broadleaf weeds such as redroot26 April 1990
pigweed and lamb’s-quarters, are a serious problem
in cabbage production in Massachusetts and can
significantly reduce yield if uncontrolled. Post-
emergent-herbicide use is not commonly used for
cabbage weed control in Massachusetts; only re-
cently has a suitable herbicide become available to
growers. Since an early planting date is regarded
as critical, growers are advised to use early trans-
plant varieties of cabbage and to apply preemergent
treatment with herbicide at a recommended rate
(Gillmeister, Moffitt, Bhowmik, and Allen).
Because of a number of concerns related to her-
bicide use, multiplot-multiyear testing was con-
ducted at the University of Massachusetts to
investigate the relative effectiveness of different
preemergent-herbicide treatments (Bhowmik 1982,
1983, 1984). Experiments involving control strat-
egies based on preemergent herbicidal treatment
provided observations on cabbage yield and weed
weight corresponding to the different strategies. A
total of eighty observations were obtained for use
in estimation (Gillmeister).
The parameters in equations (2) and (3) were
estimated by the method of maximum likelihood
using the experimental data described above. Pa-
rameter estimates ar~ Y. = 20,598 (18.84), d =
20.651 (5.93), and (3 = 2.68 (3.32), where num-
bers in parentheses are estimated asymptotic t-sta-
tistics. An average cabbage price of $0.20/kg (U.S.
Department of Agriculture), trifluralin price of
$14.20/kg ai (Agsystems Research), and fixed ap-
plication cost of $22.05/ha (University of Massa-
chusetts Cooperative Extension) were used along
with the estimated technical parameters. Time-se-
ries cross-section observations involving no weed
control were used to obtain estimates for w and CJ2
of 563.15 kg/ha and 175,710 kg/ha, respectively.
Currently, a treatment rate of 1.12 kg/ha is rec-
ommended for trifluralin.
Parameter estimates were used to maximize (5)
to determine the threshold and level of control for
the preemergent-herbicide triflurrtlin. The neces-
sary conditions for determining the threshold and
level of control for trifluralin are determined in a
straightforward manner (see Appendix) and are
NJARE
(6) O = U@ya(l/~) exp{(- 1/2 ~)
* ((vhT + f – W@ 1 – exp( – fUh)l)@d1
—exp( – jlh~)])2 – l%} + (@PY~ exp( – ~h~)
— v) * {1 – Q[(vh~ + ~ – ~pya * [1 – exp
(- PZT)IYUPYC41 - exp( - L%)]]},
(7) 0 = W, – (vhT + jYpy~[l – qi-t%)l.
Table 1 shows the level of control, threshold,
and expected profit for” schedule spray” preemer-
gent herbicidal treatment and the threshold treat-
ment strategy defined earlier. The expected value
of cabbage weed information corresponding to the
latter is also shown in the table. As is evident,
early season weed information can have substantial
value, perhaps as much as $175 per hectare.
An important caution related to the value esti-
mate should be noted. The optimal treatment rate
associated with the threshold-type management
strategy is larger than the currently recommended
treatment rate. Possible phytotoxic (Ellis and 11-
nicki) and/or environmental concerns may place
constraints on treatment rates, thereby reducing the
value of weed information in implementing a con-
trol strategy. To investigate information value in
this circumstance, (5) was maximized constraining
the treatment rate to not exceed the recommended
rate. As shown in Table 1, expected profit in this
case is $4,037 per hectare with expected weed in-
formation value of$71 per hectare, Hence, early
season weed information appears to have potential
value even if the preemergent treatment rate is con-
fined to the current recommendation.
Concluding Remarks
Because of concerns about both groundwater qual-
ity and food safety, reducing the routine use of
preemergent herbicides may become art increas-
ingly important component of weed-management
strategies in the years ahead. Economists can par-
ticipate in this process by assisting in the devel-
opment of environmentallysound weed-management
strategies that are based on knowledge of and sen-
sitivity to implications for the farm economy. The
Table 1. Management Strategy, Expected Profit, and Expected Value of Information
for Cabbage Weed Control in Massachusetts
Expected Value of
Expected Profit Weed Information
Management Strategy ($/ha) ($/ha)
AppIy a preemergent trifturatin treatment at 1.12 kg/ha. 3,966
If weed weight exceeds 13.07 kg/ha, then apply a preemergent tnflrrralintreatment at
—
2.32 kg/ha; else do not control. 4,141 175
If weed weight exceeds 9.67 kg/ha, then apply a preemergent tritluralin treatment at
1.12 kg/ha; else do not control. 4,037 71Gillmeister, Mo@t, Bhowmik, and Allen Information Va!ue in Weed Management 27
economic potential of early season weed infor-
mation was explored in this paper as a herbicide
substitute in cabbage weed control with promising
results, However, much more empirical work is
needed to provide a basis for focusing research
activities and developing weed-management alter-
natives.
References
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issues,
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Appendix
Derivation of equations (5), (6), and (7) in the text is
indicated below. Notation is the same as in the text.
E[rI] = m I W(S < WTI “ Pr[wos WA
+ EIII I W. > WT] . Pr[Wo > WT]
rw.
— —J
-(pyYo- p, a WO)(U(W a))
.-
exp ((– l/(2u2)) (W. – p,)2)d W.
/
.
+ ~T@Y Yo – P, rS Wo exP(– ~~T) - “hT - fl
(l/(fi u)) exp(( – l/(2CT2))(WO – p)’)d WO
‘( )
w~–p
=py Yo@ ~ –pycl
J
WT
Wo( l/(V% u)) exp(( – l/(2u2)) (W. – p)’)d W.
.-
– p, a exp( – ~hT)
J-
WO(U(V% u))
WT
exp(( – l/(2u2)) (W. – p)2)d W.,
which reduces to equation (5) in the text. Differentiation
with respect to hTand WT gives
~. -v[l- @(v) d E[H]
(wT-~)2)+b’(w)l
+ (3 py a exp( – f3hT)(ak%) exp(( – l/(2u2))
and
d E [II]
— = (p, Y“ - p, a WT) (l/(v% u))
a w.
t!xf)( – (1/(2u2)) (W’T– ~)2)
- @YYo ‘Py~WTexP(-~h~) - vhT ‘fl
. (l/(@ ~)) exp( - (1/(202)) (W7’- W)*).
Setting derivatives to zero and solving simultaneously
gives equations (6) and (7), respectively, in the text.

A Computable EconomicThreshold Model for Weeds in Field Crops with Multiple Pests, Quality Effects and an UncertainSprayingPeriod Length.”

An Economic Threshold Model for Weeds in

Annual Weed Control

BioeconomicModelingto SimulateWeedControl Strategies for Continuous Corn.

Cooperative Extension. “Whole Farm Budgets,

Department of Agriculture. Agricultural Marketing Service. “Boston Fresh Fruit and Vegetable Wholesale Market Pricesand Arrivals.” USDA/AMS/F&UD/MNB,1987.

Developing Weed Control Recommendations for Farmers.”

Economic Impact of Public Pest Information: Soybean Insect Forecasts in Illinois.”

Economic Thresholds Under Uncertainty with Application to Corn Nematode Management.”

Evaluation of Herbicides for Weed Control in Early TransplantedCabbage,” and “Evaluation of Herbicides and Cultivation for Weed Control

INFORMATION VALUE IN WEED MANAGEMENT

INFORMATION VALUE IN WEED MANAGEMENT

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