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WPTC 06-04
I '-ional Agricultural Trade and Policy Center
TECHNOLOGY ADOPTION AGAINST INVASIVE SPECIES
By
Ram Ranjan
WPTC 06-04 May 2006
WORKING PAPER SERIES
'V
i~fr
UNIVERSITY OF
FLORIDA
Institute of Food and Agricultural Sciences
INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
THE INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
(IATPC)
The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multi-disciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:
* Serve as the University-wide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nation-wide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.
Technology Adoption against Invasive Species
Ram Ranjan
Postdoctoral Associate
International Agricultural Trade and Policy Center
Department of Food and Resource Economics, University of Florida
Email: rranjan(@ifas.ufl.edu, Ph: (352) 392 1881-326; Fax: (352) 392 9898
Selected paper prepared for presentation at the AAEA Annual Meeting in Long Beach
California 2006, July 23-26, 2006.
Copyright 2006 by Ram Ranjan. All Rights Reserved. Readers may make verbatim
copies of this paper for non-commercial purposes by any means, provided that this
copyright notice appears on all such copies.
Abstract
This paper explores the issue of technology adoption in agriculture that is
specifically targeted against invasive species. The analysis involves predicting the long
term distribution of technology choices when technology can be adopted and dis-adopted
based upon current and expected agricultural profits which are influenced by the state of
pest infestation. The impact of adaptive learning on adoption of technology is analyzed
in the setting of complacency set in from a reduction in risks or compulsion to adopt
technology from reduced profitability in event of non-adoption. Possibility of eradication
of the disease based upon long term adoption of technology is also explored. The
theoretical analysis confirms the intuition that psychological factors such as complacency
may have a significant impact on technology adoption and hence disease eradication.
Further, learning from neighbors may not necessarily lead to higher technology adoption.
In fact, overall adoption may go down based upon the level of complacency prevalent in
masses. An empirical application is performed for the case of soybean rust. Findings
indicate that the role of psychological perceptions may play a role in disease spread in the
short run. The long term spread and establishment of the disease would be determined by
nature and speed of the learning process for the farmer over the pest's optimal
management strategy.
Keywords: soybean rust, technology adoption, invasive species, complacency, and
compulsion
1. Introduction
Several features differentiate technology adoption specifically targeted against invasive
species from the conventional technology adoption geared towards increasing
productivity in agriculture. For one, the adoption and dis-adoption of technology may be
correlated with pest population. A reduction or elimination of pest population may lead
to dis-adoption of that technology. Second, technology itself may continue to change
faster than the rate of adoption due to the need to incorporate resistance/control of
multiple pests, consumer reaction, productivity effects, etc1. Finally, technology
adoption in conventional agriculture is geared towards attaining higher profitability,
whereas the immediate aim of technology adoption against invasives is mostly
preventative in nature and therefore is subject to fluctuations borne out by adopter's
psychological responses such as complacencies or compulsions.
Technology adoption is significantly influenced by learning by doing or
observing, as has been argued in the literature. However, in case of adoption of a new
technology in order to ward off a threat from invasion species, complacency may play a
crucial role in determining its extent of adoption and consequently decide the eventual
eradication or establishment of the pest. Geoffard (1997) points out that vaccination
demand for diseases such as tuberculosis, influenza, etc. falls as the prevalence of the
disease in the population falls. This phenomenon, characterized as the prevalence effect,
may also be found in the case of invasive species that threaten agriculture. Farmers,
whose crops have not yet been infected with invasive species, might wait until the pest
1 For instance, the ability to include productivity enhancing genes along with pest-resistant features in
soybean requires a larger genetic pool. Other desirable features may include those that enhance its
consumer-desirability, such as low-saturated fatty acids and higher protein contents. Resistance to abiotic
forces is also a desirable feature as it enhances productivity.
arrives as close to the neighbor's farm. This complacency may also be aggravated by the
presence of government indemnity programs and insurance schemes that aim to
compensate the farmer in the wake of damages from infestation, without imposing good
farming practices. Empirical work on measuring or explaining the extent of complacency
effects is still missing, but its existence has also been discerned in several other fields.
Sterman and Booth Sweeny (2005) argue that one reason people do not show any sense
of urgency when it comes to global warming is due to their 'difficulty in relating flows in
and out of stock to the trajectory of stock'. Consequently, the stock of carbon is
understood to be falling with reduction of emissions, even as the net inflow into stock
may be positive. This behavior is also explained by pattern matching heuristics (Sterman
and Booth Sweeny 2002). Complacency against infectious diseases may have similar
origins; people relating a reduction in pest infestation rate to a reduction in the total
infested population. No matter what the basis for complacency, the fact of its existence
cannot be overlooked.
Opposite to complacency effect, certain factors such as the influence of
neighbor's actions on one's own profitability might compel technology adoption. For
instance, precision application of fungicides to soybean rust in a certain location reduces
the risks in the applied areas, but significantly increases the risk of infestation in the
neighborhoods where such applications have not been made. This may have a positive
cascading impact on such kinds of technology adoptions. Whether or not forces
influencing technology adoption are of 'complacency type' or 'compelling type' would
depend upon pest characteristics, its modes of transport, and several other regional, social
and behavioral factors.
In this paper we look at the issue of technology adoption in agriculture that is
directed towards combating invasive species. We build on the previous literature on
technology adoption that highlights the role of adaptive learning in the process of
technology adoption (for instance Ellison and Feudenberg 1993 &1995). Role of public
communication such as mass media and interpersonal communication such as between
neighboring farmers, input suppliers, and regulatory agents has been crucial in
determining the spread and adoption of new technologies in agriculture. While mass
media creates awareness, interpersonal communication is more crucial in transferring
technical knowledge to farmers (Longo 1990).
The analysis in this paper involves looking at the long term distribution of
technology choices when technology can be adopted and dis-adopted based upon current
and expected profits in agriculture. The impact of adaptive learning on adoption of
technology is analyzed in the setting of complacency effect set in from a reduction in
risks or compulsion to adopt technology in wake of reduced expected profitability from
not doing so. Possibility of eradication of the disease based upon long term adoption of
technology is also explored. The theoretical analysis confirms the intuition that
psychological factors such as complacency may have a significant impact on technology
adoption and hence disease eradication. Further, learning from neighbors may not
necessarily lead to higher technology adoption. In fact, overall adoption may go down
based upon the level of complacency prevalent in masses.
An empirical analysis is also performed for the recent case of soybean rust advent
into the United States2. Even though the pest has arrived into the US, the infestation rates
2 In terms of soybean yield differences amongst farmers, technology adoption has been believed to be a
deciding factor. Those farmers who are able to exploit better technology can produce soybean at a cost of
so far have been fairly low. However, significant threat exists for future cases of severe
infestation if adequate preventative measures are not taken into account. This threat is
further compounded by extreme weather events such as hurricanes that are capable of
transforming soybean spores to far off places. Due to the spatial and temporal
differences in soybean infestation within the various soybean growing regions of the US,
there is a significant scope for learning from infestations and treatment results within the
neighboring States. Consequently, psychological perceptions may play a role in disease
spread in the short run. The long term spread and establishment of the disease would be
determined by nature and speed of the learning process for the farmer over the pest's
optimal management strategy.
2. Model
Let there be two technologies, an existing one (f) and an alternative one (g) that is
supposed to be more effective against invasive species. Technology g could be thought
of as a pest resistant variety of crop that is available to the farmer, or a better
management practice involving timely fungicide applications. The difference in the
payoffs between these two technologies is given by: Ug -U > 0 + where 0 is the
deterministic component of payoff differential and c is the stochastic component with a
uniform distribution. Following the mathematical approach in Ellison and Feudenberg
(1993), we assume that the farmers' decision to adopt technology g is based upon a
popularity weighting scheme that influences their decision to switch. This scheme is
given by: m(1-2x), where m is the popularity weight assigned to the proportion of
$2bu/acre as compared to $10bu/acre for those who don't (Wherspann 2003). In general, the rate of
technology adoption has been found to be quite significant in agriculture in certain areas. Fernandez et al.
(2003) find that the adoption of herbicide tolerant soybeans rose from 17 percent in 1997 to about 81
percent in 2003 for the United States.
farmers (x), who have already adopted the better technology. The farmers' decision
problem is then to: Choose g if Ug U > m(1 2x). Notice that under this kind of
selection scheme, the more popular technology will be selected even if the current payoff
from that technology is low. This is evident by substituting values of .5 or more for x in
the above equation, which turns the right hand side negative.
We incorporate complacency effect by initially assuming that complacency sets in
with an increase in the proportion of farmers adopting the better technology. This kind of
assumption is justified in cases where an increase in the level of adoption has a negative
influence on rate of infestation, thus reducing its risk of further spread. When this
happens, a marginal increase in adoption of technology would require a higher
differential in payoffs between the two technologies as the farmer is now reluctant to
switch to the better technology if the threats have reduced. This possibility would lead to
switching when: U U > m(- 2x) q(- kx), where q is the parameter that
influences the level of complacency and k determines the level of adopted population
beyond which complacency sets in. Following the analysis in Ellison and Feudenberg
(1993) we derive the dynamics of agricultural technology adoption and conditions for full
technology adoption. Ellison and Feudenberg (1993) assume that in each period due to
inertia, only a fraction of the population, given by a, is able to make the choice of
whether or not to switch. In the case of invasive species, this can be thought of as a
spatial parameter which may relate to the proximity of the population that is up for
choice, to the population that has already adopted the better technology. The increase in
population that adopts the technology is then given by the rule:
(1) x(t + 1) = x(t) + a(1- x(t))- > P[1- H(m(1 -2x)- q(1 -kx)- 0)]
whereH is the cumulative distribution function of the random term Growth in x is
determined by the probability that the random element of the profit, s, is at least larger
than the popularity and complacency weighted deterministic element of profits.
Similarly, the conditions for a downward movement in x are given by:
(2) x(t +1) = (1- a)x(t)- > P[H(m(1 2x) q(1 kx) 0)]
Following Ellison and Feudenberg (1993), level of x, sayxg beyond which the better
technology is certain to be adopted is given by:
(3) 0 + E > (m(1 2x) q(1 kx))
Which can be derived noting that x is certain to move forward if the minimum value of
payoff is positive. This is possible when = :
(4) x(t) > xg a > m(l1- 2x) q(1 kx)
which gives:
0-+m-q-0
(5) xg > -+m-q-0
2m -qk
Similarly, the value of x, say xf below which a backward step takes place with certainty is
derived as :
(6) x(t) < xf 0 + a < m(1 2x)- q(1 kx), which gives:
(7) xf (m q -0 o-)
2m qk
Also, realizing that the minimum probability of an upward step is possible when x=0, we
get this probability as:
(8) P(O + E > m q), or,
-m++q xf (2m qk)
(9) P[O +> m q] = =
20c 20c
Similarly, the minimum probability of a downward step is realized when x=l:
(10) P(O + e < -m q + qk), or,
(11) P[ m q- -0 + qk q (xg 1)(2m qk)
(11) P[0+e
20 2c
From above Ellison and Feudenberg derive the conditions for convergence of the
technology as:
(12) xg < 1, xf < 0 => x(t) 1
(13) xg > 1, xf > 0 => x(t) 0
(14) xg > 1, xf < 0 => no convergence
(15) xg <, xf > 0,if x, > xg => x(t) = 1, however if x, < xf => x(t) = 0
Condition (12) implies that the better technology will eventually get adopted if
2(m q)- 0
xg < xf <0 Also note that when q = c, and q < 2: xg < <1, and
2m- qk
x -(m-q-0- ) < 0 Therefore, when the popularity weighting impact net of any
2m -qk
complacency impact equals the maximum range of the random error, the entire
population converges towards the better technology. Ellison and Feudenberg
characterize this as the optimal weighting scheme as convergence happens with
probability one. Similarly, when the popularity weighting impact net of any
complacency impact either exceeds or is less than the maximum range (o) of random
error, convergence is possible depending upon the starting point.
Now, let's derive the conditions for convergence when complacency effect
dominates popularity weighting. Specifically, the condition for a forward step with
certainty is: 0 a > m(1 2x) q(1 k)). Since, in this case q > m the lower the value
of x, the higher would be the probability of a forward jump. Therefore, a forward jump
k -m+-O
happens with certainty when: x < x' (). Similarly, a backward jump
2m + qk
m .k- +0 +
happens with certainty when: x > xf ( m + ).
2m + qk
It is obvious that the better technology will not be adopted with certainty, thus
leading to less than full convergence in the long run. Notice that, as x increases, the
probability of an upward step keeps decreasing. It can be shown that the system will
converge towards the conventional technology with positive probability if xg <0.
While the above setting assumes a linear equation between popularity and
complacency effect, thus allowing the stronger effect to dominate, complacency effect
may also be non-linear in level of adoption. For instance, low levels of adoption might
also reflect low threat from disease, thus making would-be adopters in a neighboring
region complacent. Similarly, high levels of adoption could imply a low level of disease
too due to the impact of higher adoption, again discouraging remaining would-be
adopters. Whereas, in the middle, the complacency effect could be low as would-be
adopters see significant threat from the pest. Such, a relationship, however, is entirely
governed by how pest infestation is influenced by technology adoption.
2.1 Some Extensions
Now, let us discuss some of the features that are unique to the agricultural
technology associated with invasive species. One possibility is that the benefits from the
better technology keep increasing with adoption as the pest population gets under control.
Another possibility is exactly the opposite; that of a falling differential in profits with
increasing adoption. There are several reasons why this may happen and we discuss that
in the ensuing sections. Finally, non-linearity in the profit differential is also taken up in
this section.
2.1.1 Difference in Payoffs is increasing in Adoption
The payoff differential may be increasing with adoption of the new technology if the
impact of the pest is increasing in proportion to the population using the better
technology. This is a plausible scenario as the host size for the invasive species reduces,
thereby concentrating the existing pest population on the remaining areas using the older
technology. Such a payoff differential can be thought of as being dependent upon the
proportion using the new technology as Ox.
2.1.2 Difference in Payoffs is falling in Adoption
Difference in payoffs could also be falling in profits due to several reasons. First, if the
impact of the invasive plant falls with the level of adoption, making it impossible for the
pest to establish once the host population (given by the percentage of population using
the old technology) falls below a certain threshold. Initial adopters may be compensated
for the high costs of production by the higher rewards from possible enhanced
productivity. However, as the proportion of adopters of new technology increases,
increased productivity might bring the profits down, thus making the new technology
costlier. Note that this situation may also be highly conducive for complacent behavior,
as a reduction in the difference in profits caused by reduced damages from pests
discourages adoption of new technology. Second, profits may fall if the preferences for
the old variety (using old technology) increase due to consumer skepticism and
reluctance to try new varieties. Profits may fall also from an increased supply of the
agricultural commodity in the market caused by the new technology. In certain cases the
new technology may also end up adversely affecting other pests of the commodity thus
increasing productivity (Livingston et al. 2004). If the demand for the agricultural
commodity is highly inelastic, this might cause a reduction in overall profits for every
one. Finally, heterogeneity in population given by differences in production costs would
lead to farmers with higher costs postponing their adoption until alter on. When this
happens, there may be threshold level of population for technology adoption beyond
which it is optimal for the farmers still using the conventional technology not to adopt.
Consider the possibility that the payoff differential is falling as given by: 0(1 -x).
A farmer would choose the better technology if: 0(1 x) + E > m(1 2x). Now, the value
of x beyond which a forward step is possible with certainty is given by:
m-8+c
x > xg* -- 0 The value of x below which a backward step is possible with
2m-0
-P +m-0
certainty is given by: x < x - 0 When the payoff differential remains
2m -
constant equal to 0, the same cut-offs are given as:
m-8+cr -c+m-O
x > X x < x Consequently, a falling differential shifts the
2m 2m
cutoffs towards the right as shown below. Intuitively, it becomes much easier for the
system to move towards the conventional technology and away from the better one.
Xf xf' g xg
2.1.3 Difference in payoffs is non-linear in adoption
Non-linearity in adoption may arise form several reasons. For one, if the new technology
is a biologically altered plant variety that may be resistant to pests or herbicides, its
profitability may depend upon several key factors including public preferences for the
new food, overall market size, etc. A small market for a new variety of plant may soon
get glutted with output, thus lowering prices and possibly profits. In this case, the
difference in profits between the old and the new technologies may turn from positive to
negative as the adoption level for the new technology increases. Consider the case for
consumer preferences for genetically modified and organic foods. As the level of genetic
alteration increases in the new variety of plants, consumers' skepticism may increase too,
thus making the traditional plant variety more preferable. If the supply of the traditional
variety falls, from lower population producing it, the prices may increase, thus making
lower technology more profitable. This non-linearity can be incorporated by assuming
that the payoff function is non-linear and given by: 0 Cos [ 3x]. Figure 1 below shows
the profit differential as the level of adoption increase from 0 to 1.
INSERT FIGURE 1 HERE
Next, we plot the conditions that ensure certainty of forward and backward motions. For
a given set of parameters: 0=2;o=4;k=2;m=2; Certainty of an upward movement is given
by the condition that: 0 Cos[ 3x]-m(1-2 x)-o>0. The condition for certainty of a
backward step is given by: 0 Cos[ 3x]-m(1-2 x)+o<0. This is shown below in figures 2
and 3. As is evident from the two figures above, neither forward nor backward steps are
possible with certainty for any value of x, which should be obvious given the non-
linearity in the profit function and the ensuing dis-incentive to adopt marginally at high
stages of adoption and dis-adopt marginally at low stages of overall adoption. Now, let
us consider the long term distribution of the system. For m=2;9=2;C=5; the steady state
distribution of the system between discrete states of adoption defined as:
113
x(t) = 0, ,1 is given by: 0.18,0.19,0.21,0.21,0.20. As is evident from above, all
4 2' 4
states are equally attractive in the long run.
3. Technology Adoption and Disease Eradication
Heterogeneity in the population can be present due to several reasons such as differences
in production and treatment costs, differences in the age, education and risk perception of
the population etc. However, spatial heterogeneity may be another key factor that may
have a significant impact on the level of adoption. So far in the above sections we have
concentrated upon the level of technology adoption without paying any attention to how
it may have an impact on disease spread and eradication. It is obvious that less than full
adoption may have a bearing on the long term impact of the disease and we saw several
cases above where the better technology could not be adopted with probability one. In
this section we explore the impact of less than full adoption on disease establishment
when there is spatial heterogeneity.
Consider the threat of infestation that affects two regions: x and y. Region x is the
follower whereas region y is the one impacted first. Region x demonstrates complacency
in adoption which is given by: 0 + E > m(1 2x) q(1 2y). This complacency in
adoption is not only based upon adoption within region x but also influenced by the level
of adoption in region y as given by the parameter q. Notice that, as the level of
technology adoption within region y increases, the threshold for adoption within region x
falls at first, but once the level of adoption crosses half, the threshold level of adoption
within x starts increasing in y. This captures the complacency that may set in from a
temporary reduction in pest threats due to a higher level of adoption in the frontier region
y. Region y has the standard response as: 0 + E > (m(1 2y). Probability of a forward
step for region x is given by:
S+ + q(1 2y)- m(1 2x)
(16) P[O + E > (m(1- 2x) q(1- 2y)] =
20
Probability of a forward step for region is given by:
0- + m(1 2y)
(17) P[O + e > (m(1 2y)] =
20c
Now, in order to look at the steady state distribution of the system, we divide the state
space into nine parts as follows:
(18) { xOyO, xOy.5, xOy, x.5yO, x. 5y.5, x.5y, xyO, xy.5, xy}
The transition matrix representing the probability of transition between these nine states
is shown in the Appendix. For parameter values (o =5; 0=2; m=2; q=l), the steady state
distribution in these nine states is given as:
xOyO xOy.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(19)
.0059 .0166 .1426 .0067 .0178 .1557 .0570 .0818 .5155
Notice that the system has a high propensity to settle in the state when both the regions
adopt the technology. Now consider a higher complacency effect in region x from
adoption in region y. This is given by parameters: (- =5; 0=2; m=2; q=4); the steady
state distribution is now given as:
xOyO xOy.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(20) 097 .0592 .5546 .0067 .0083 .1315 .0531 .0486 .1277
.0097 .0592 .5546 .0067 .0083 .1315 .0531 .0486 .1277
Notice that the propensity of the system to spend time in the last state when x and y have
fully adopted has fallen drastically. Consider now, a scenario where profits are
influenced by the level of adoption. More specifically, profits increase as the level of
adoption increases in both the regions. We define parameters tl...t9 that replace 0
depending upon the level of adoption in the two regions combined. The new set of
parameters is:
sigma=5;theta=2;m=2;q= ;tl=0;t2=. 5;t3=;t4=.5;t5=1;t6=1.5;t7=1;t8=1.5;t9=2;
The steady state distribution (say for the base case) is now defined as:
xOyO x0y.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(21)
.0384 .0409 .1581 .0270 .0259 .1273 .0915 .0822 .4083
Obviously, an increase in profitability from adoption provides added incentive to adopt as
is evident from the new steady state distribution. When profits are falling in adoption,
which could happen due to an increase in productivity from a better technology adoption,
there may exist an incentive not to adopt. For the parameters:
Sigma=5;theta=2;m=2;q= ;tl=2;t2=1.5;t3=1;t4=1.5;t5=1;t6=.5;t7=1;t8=.5;t9=0; the
steady state distribution is given as;
xOyO x0y.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(22)
.0316 .0589 .2063 .0414 .0517 .1388 .1523 .1201 .1984
Another interesting exercise would be to consider the impact of a higher adoption in
region on profits in region x and the subsequent impact on the long term distribution. A
higher adoption in region y may lead to an increase in productivity, thus reducing profits
in case the demand for the good is inelastic. This may have an adverse impact on
adoption in region x.
For parameters:
sigma=5;theta=2;m=2;q= ;tl=0;t2=. 5;t3=1;t4=.5;t5=1;t6=1.5;t7=1;t8=1.5;t9=2;
We consider a positive impact on region y's profits from technology adoption, but no
impact on region x's profits. That is, the values of tl...t9 are all zeros for region x,
whereas they are as given above for region y. It can be verified that the proportion of
time spent in states when region x is fully adopted falls almost to half and the proportion
of time spent in states when it is fully dis-adopted doubles from the base case.
An Application to Soybean Rust
Soybean rust, a disease of the soybean and several other plant species has been
threatening the US soybean crop since it arrived in 2004. Though the threat was reduced
in 2005 due to limited infestations during the crop season, potential for the pest becoming
endemic are serious and call for long term planning to manage this pest. Soybean rust is
chiefly windborne and is capable of trans-continental migrations helped by favorable
events such as hurricanes. In fact, hurricane Ivan of 2004 is suspected as medium for
bringing soybean rust from South America3. Soybean rust could cause significant
damages to the US soybean crops, and available estimates in the literature project losses
of up to US $7.2 billion/year from the disease (APHIS USDA 2004).
Management of soybean rust would require significant private participation
involving soybean growing farmers in the States in order to monitor and control its yearly
migration across regions. Due to its ability to survive in cool and wet climates, it is
possible for the rust to over-winter in the Southern Sates and infest soybean crops during
3 "The most likely scenario as to how soybean rust arrived in the continental United States is via Hurricane
Ivan. Ivan formed in the Atlantic in early September, brushed the South American coast, and proceeded to
strike the southeastern United States, carrying rust spores from Colombia and Venezuela". (Hart 2005).
the growing season. Kudzu, a secondary host of the rust, is predominantly found in the
Southern States and could greatly assist in the long term establishment of this pest.
Management of soybean rust would require understanding the cropping decisions of the
farmers and being able to influence it through public policies. Crop rotations, such as
switching between soybean and corn and adequate precautionary steps such as spraying
of plants with fungicides could significantly diminish the damages from soybean rust.
Yet, crop rotations are a function of several economic criteria such as differential
economic yield between various crops per acre, yield drags and additional input costs
involved in sub-optimum crop rotations and the risk perception of the farmers. Similarly,
decision over how much or whether or not to spray are influenced by risk perceptions and
could vary from location to location based upon farmer and regional heterogeneity.
Adaptive management of crops faced with threat of invasion can be expedited by public
polices that reward socially optimum practices. For this to be possible, an understanding
of farmer's learning capabilities under various infestation scenarios is crucial as it would
help policy makers be a leg up in terms of public inducement programs.
Herein, we select two regions, the Mississippi delta and the US Heartland for
analysis. The total average profits for the years 2003 and 2004 in the two regions, net of
operating cots, are presented in the tables below. The range of profits in the various
scenarios of infestation, no-infestation, treatment and no-treatment is calculated and
assigned a uniform distribution. Consequently, it is assumed that the probability of
adoption is positive whenever the profits are in the non-negative range. For simplicity,
we assume that currently there are no complacency effects. Next, we look at the adoption
of treatment technology for the region of Mississippi. When adoption inertia is low, state
space is defined as the fraction of population that has adopted the spraying technology in
any given time period. Let 0 < x(t) <1 be the fraction of people who have adopted the
new technology at time t. There is inertia in the system as a result of which only a
fraction of the population can adopt or reject the new technology per unit of time. More
specifically, the fraction of people using the new technology can take the following
possible steps:
113
(23) x(t) = 0, ,1
4'2'4
The choice of the better technology is based upon adaptive learning, and farmers switch
to a better technology if the profits from adopting that technology in the previous period
are positive and given as: 0+c, where c is a randomly distributed variable. The
probabilities of forward and backward steps are given by:
1 1
p(x( ) x( )) = p( > -0)
(24) 4 2
1 1
p(x() x(-)) = p( <-0)
2 4
Using the above assumption, we derive the steady state level of adoption of technology
for the Mississippi region as given below:
0 1/4 1/2 3/4 1
(25)
.0005 .0033 .0212 .1335 .8413
Note that in the long term, the entire region of Mississippi would end up adopting the
technology 84 percent of the time. This is slightly lower than the probability of adoption
as derived in table 1. When adoption inertia is low, we can assume that a larger fraction
of the population makes the decision to adopt the spraying technology in any given time
1
period. Let the new state space be x(t) = 0,-,1, following which the long term steady
2
state is derived as:
0 1/2 1
(26)
.021 .134 .845
Notice a slight increase in the fraction of time when the entire population ends up
adopting the new technology. In fact, as the inertia falls, the long term steady state
fraction of time would end up equaling the probability of adoption.
Now, let us consider the case when adoption of technology in one region
influences adoption in the other region. Farmers in the Heartland region (see Table 2)
wait and watch the advent of soybean rust in the Mississippi region each year and based
upon the level of infestation and the measures taken by Mississippi farmers, form opinion
over the risk of spread into the Heartland region. Following the model in section 3, we
assume that the farmers in the Heartland region have a complacency effect which kicks in
whenever the technology adoption level in the Mississippi region reaches a certain
threshold. Using the profits, net of variable costs, as derived in the tables; we design the
long run steady state distribution of technology adoption within the two regions. The state
space is defined as:
(27) xOyO xO y.5 xOy x.5 y x.5 y.5 x.5y xy 0 xy .5 xy
where xOyO stands for the fraction of time when both regions show zero adoption.
For Mississippi, a = 91.25 0 = 66.26, m = 0, and for the Heartland
a = 85.012,0 = 60.012, m = 0,q = 0. The steady state distribution is now derived as:
(28) xOyO x0y.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
.0005 .0033 .0206 .0030 .0192 .1209 .0179 .1116 .7026
Notice that when complacency effect is assumed to be zero, both the regions end up
adopting the spraying technology seventy percent of the time. Now let us increase the
popularity weighting factor m to 2. For Mississippi, o = 91.25 0 = 66.26, m = 2 and for
the Heartlando- = 85.012 0 = 60.012 m = 2 q = 1, the steady state distribution of times
spent in each of these states is now derived as:
xOyO x0y.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(29)
.0005 .0031 .0213 .0026 .0172 .1182 .0171 .1046 .7151
An increase in the popularity weighting factor leads to an increase in the fraction of time
spent in the state when both regions are fully adopted. When the complacency effect for
the Heartland region is increased to q=20, the steady state distribution of times spent in
each of the states is now given as:
xOyO x0y.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(30)
.0007 .0086 .0635 .0028 .0257 .1897 .0168 .0906 .6012
When the complacency effect for the Heartland region is increased to q=60, the steady
state distribution of times spent in each of the states is now given as:
xOyO x0y.5 xOy x.5y0 x.5y.5 x.5y xyO xy.5 xy
(31)
.0012 .0315 .2335 .0045 .0340 .2764 .0148 .0596 .3444
Notice now that an increase in the complacency effect leads to a dramatic fall in the
fraction of time spent in the state when both regions are fully adopted. Also note that
region x shows strong negative correlation with region y in terms of fraction of
population that has adopted the technology. For instance, when y is fully adopted, the
probabilities of region x being fully dis-adopted or fifty percent adopted are .23 and .27
respectively.
The above analysis assumes that level of adoption in the Mississippi region has no
impact on the level of pest infestation. Similarly, the long term pest infestation may be
determined by the level of adoption in both the regions and it is likely that over time the
distribution of profits would shift towards the positive side with continued adoption and
towards the negative side with low levels of adoption. But, at this stage there is not much
empirical evidence to incorporate the endogeniety in probability of adoption brought in
by its impact on pest population.
While complacency is one aspect of technology adoption, compulsion may have
an equally significant role to play. If farmers insure themselves against pest damages,
good management practices require that they spray their crops with fungicides whenever
it is required. Failure to follow this protocol might lead to loss in compensation payment
from the insuring agency. Also, if spraying by the neighbor increases the risk of
infestation on one's own fields, the farmer might be forced to adopt spraying.
Conclusion
Technology adoption against invasive species is guided by several motives as has been
demonstrated in this paper. Psychological factors such as complacency and learning
from neighbors could play a crucial role in this process. The existing literature on
technology adoption does not provide much guidance over the long term state of
technology adoption against invasive species. Yet, long term adoption rates are very
significant to understand from policy perspective as they determine whether or not a pest
will become endemic.
In this paper, we demonstrated that technology adoption may not be fully realized
due to several factors. Chief amongst them are compulsion and complacency. Other
factors that feed into these effects are dependent upon the unique characteristics of the
invading pests. The application to soybean rust portrays a good possibility of these
effects showing in and influencing the technology adoption processes. Very little is
observable in terms of actual technology adoption at this stage due to the nascent nature
of pest infestation, but chances are good that compulsion effect might dominate the
complacency effect. This is due to the heavy damages caused by soybean rust in Brazil
and the observed behavior of soybean growers in the US so far who have demonstrated a
very keen interest in keeping track of the day to day migration of rust spores over the
United States. Much work remains to be done in terms of eliciting farmer's response to
soybean rust outbreaks in his neighborhood in order to be able to understand adoption
behavior. With a large number of pest invading same crops in future, due to increasing
rates of alien infestation in the US, it is likely that the rate and nature of technology
adoption by farmers would become a more complex process not easily discernable. It is
very likely that farmer types characterized by size of farm, education, income, etc. would
have an increasingly key role to play in determining who adopts and who does not.
References
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Agric. Econ. Assoc, Long Beach, CA.
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Appendix
-m+e+c -m+q++ (-m++or) (1 0t ) (-m+q+tc) (l-- G) (-m+6+o) (-m+q+e+o)
22(8+0) (1- --)2 (-m8+o*) (1- .- 0) (S+a) (-m+e+o c) O, O, 0}
S +-e ), o, 0, 0 0, 0, ,
S27 ( 20 200 20 402
+, +e +o ( -m-q+eS+ (m+e+o) (1-- )
0, 1--2-) 1-' 2 '
(-m-q+e+o) (1--- ) (m+e+* ) (-m-q+e+u) 0
2 4, l,2
20 402
-m+ q+e+c (-m+ +o) (1- ) (q+e+o) (1- (-m+)+) (q+e+o)
1- -- 1_ 0, 0, 0, 02 4 O ,
2 2u 2a 2a 402
e+0 2 e+0 (+0) 21 e c- e) (e+o)2
{(1 o 0, 2 a ), 0, 0, 0, (o I 0, ,
m+e+ -q+e+o (m+o+)(1- )(-q+e+c) (1- ) (m+e+o-) (-q+e+o2)
{0, 1 -C 2 a 0, 0, 0, -42
2c 2o 2a 2, 4c2
-m+ mmq+6 (-m+(+iq) (1- 2--- )
0, 0, 0, (1--m+ 1- m, +c +l2
I ~l 2a 2o 2o
,O (m+q+e+o) (1- (-m+ ) (m+q+e+o)
12o 2402 '
2o ..(..- 0 2e+-1-0 'O (m+ +a) (1- I (..o)
, O 2o 2o )' 2o 2o 4o 2 '
m+e+o) m-q+e+ (m+e6+) (1- 2o)
20, 0, 0, 1- 2a- 21 -
I '\ 20, ; 20 2o
(m-q+e+0) (1- +18.)
(m-q + ) (1 (m+e+o) (m-q++o0)
20 402
Note: This is a 9X9 matrix where each row is represented by a parenthesis containing 9
elements. The nine states of the system are given as:
{x0yO, xOy.5, xOy,x.5y0, x.5y.5, x.5y, xyO, xy.5, xy}
Mississippi Treat No-Treat Difference
Not-Infested 165.93 190.93 -25
Infested 157.51 0 157.51
Range of Difference 182.51
F(d)-U .005479
P(adoption) .863028
P(disadoption) .136972
Table 1: Adoption Data for Mississippi
Heartland Treat No-Treat Difference
Not-Infested 152.97 177.97 -25
Infested 145.02 0 145.02
Range of Difference 170.02
F(d)-U .00588
P(adoption) .8529
P(disadoption) .1470
Table 2: Adoption Data for Heartland
2
1
0.2 0.4 0.6 0.8 1
-1
-2 -
Figure 1: Profit Differential with a Change in the Level of Adoption
-2.5
-2.75
-3
-3.25
-3.5
-3.75
_- x
0.2 0.4 0. 0.8 /1 1.2 1.4
-4.25
Figure 2: Certainty of a Forward Movement
5.5
5.25
5
4.75
4.5
4.25
0.2 0.4 0. 0.8 /1
3.75
Figure 3: Certainty of a Backward Movement
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