Estimating the Value of an Early-Warning System

Review of Agricultural Economics—Volume 31, Number 2—Pages 303–329

Estimating the Value of anEarly-Warning System

Michael J. Roberts, David Schimmelpfennig,Michael J. Livingston, and Elizabeth Ashley

An early-warning system generates economic value to the extent that it improves decisionmaking. The value of the information hinges on the degree to which a timely response,aided by warnings, facilitates successful damage mitigation. USDA’s Coordinated Frame-work for Soybean Rust includes a network of sentinel soybean plots and wild kudzustands monitored by extension agents for the presence of soybean rust, a potentially recur-ring threat to the U.S. soybean crop since 2005. The linchpin in this early-warning systemis a website that provides near real-time, county-level information on the location of thedisease. We consider factors that may influence information value.

Information is valuable when it allows decision makers to adjust their actions tobetter suit the situation at hand. When information allows many individuals to

improve their decision making, a governmental role in its provision may be justi-fiable, because individuals may be unable to coordinate and finance its collectionand dissemination. Of course, just because information can embody the publicgood attributes of nonrivalry and nonexcludability does not necessarily imply arole for public policy. One must still consider social costs and benefits.

While cost calculation might be relatively straightforward, valuing informationcan be challenging. In this paper, we consider an illustrative example providedby a recent USDA-led effort to provide real-time information for a new threat tothe U.S. soybean crop, Phakopsora pachyrhizi, a fungus that causes soybean rust(SBR). SBR, a recurrent problem for soybean producers in much of the southernhemisphere, was first detected in the United States in 2004, late enough in thegrowing season that it posed no threat to that year’s soybean crop. After overwin-tering in southern states along the Gulf of Mexico, SBR posed a new, uncertain,

� Michael J. Roberts, David Schimmelpfennig, and Michael J. Livingston are with USDAEconomic Research Service.� Elizabeth Ashley is at the Department of Economics, University of California at SantaBarbara.Views expressed are the authors’ and not necessarily those of the USDA.

DOI: 10.1111/j.1467-9353.2009.01439.x

304 Review of Agricultural Economics

and potentially severe threat to the U.S. soybean crop at the beginning of the 2005growing season (Skokstad).

The USDA-led framework provides real-time SBR information via a website(http://www.sbrusa.net) that reports findings from sentinel plots where expertsregularly monitor for soybean rust. Findings are pooled together with weatherforecasts and aerobiological analyses to forecast the likely future spread of thefungus. The overarching purpose of the framework is to provide farmers withsufficient notice so they can make appropriate decisions as to the use of preventiveand curative fungicides on their soybean fields.

In the three full years since its first detection in the United States, SBR hasposed little threat to the U.S. soybean crop. Given the expense of developingthe website and its underlying infrastructure, some have questioned whether theframework was a worthwhile endeavor. After all, if farmers had simply managedtheir crops as if there were no SBR threat, they may have fared as well or bet-ter than they did in the presence of the Coordinated Framework. However, thisview overlooks a key point: although weather conditions have not yet facilitateddispersion of SBR spores to key soybean-producing regions, this could not havebeen known in advance. A potential SBR threat existed at the beginning of the2005 season, but how farmers might have prepared for that threat in the absenceof the USDA framework is not clear. Indeed, without the framework, individ-ual farmers may have incurred even greater expense by monitoring their ownfields, perhaps spraying fungicides for a threat that did not exist in their area, orforgoing planting entirely.1 More generally, this view overlooks the fundamentalnotion that information value should be assessed from an ex ante perspective.Quantifying the ex ante value involves determining the expected value of actionswith and without the benefit of information and subtracting the latter from theformer. This can be challenging because it involves determining decisions thatwould have been made without the information, and what the consequences ofthose decisions would have been. Perhaps more elusively, it also hinges on whatfarmers’ expectations would have been without the USDA framework.

We develop estimates of the ex ante value of information provided by the USDAframework from the vantage point of the beginning of the 2005 growing season(Roberts et al.). We show how various factors influence the size of this value, in-cluding the costs and efficacy of available fungicides, farmers’ prior beliefs aboutthe likelihood of infection, the perceived accuracy of the framework’s SBR fore-casts, and farmers’ risk preferences. The value may also depend on how soybeanprices would be affected by SBR-induced production shocks. Our analysis buildson standard Bayesian decision theory.

Most empirical value-of-information studies consider only the value of perfectinformation. In this study, we develop a set of assumptions that allows us toconsider the value of information over a continuum of information qualities.This is useful in gauging the value of more realistic information systems. It alsofacilitates straightforward valuation of marginal improvements in informationquality.

We find the value of information depends on many factors, but most impor-tantly farmers’ prior beliefs about SBR risk at the beginning of the growing sea-son and the accuracy of the system’s forecast. These factors cannot be quantifiedprecisely, so we consider information values over a range of assumptions aboutprior beliefs, forecast accuracy, and other factors. Even if forecasts are imprecise,

Estimating the Value of an Early-Warning System 305

resolving only 20% of SBR infection uncertainty for all fields planted with soy-beans, the system’s value in 2005 was an estimated $11 million. If forecasts re-solved 80% of infection uncertainty, the estimated value was $395 million. Ouranalysis suggests that the value of the information in 2005 likely exceeded costsof developing the information, reported to be between $2.5 and almost $5 million.

Three additional factors affect estimated information values: anticipated priceshocks in the event of a large rust outbreak, soybean farmers’ aversion to risk,and heterogeneity of farmers’ prior beliefs of an infestation. We find that all ofthese factors tend to reduce the largest estimated values and increase the smallestestimated values, but the effects are relatively small in magnitude. The potentialbenefits of the framework suggest that similar programs for other crop pests canbe cost effective if, as in the case of soybean rust, preventive action can stronglymitigate damages in the event of an outbreak.

Bayesian Updating with Information AccuracyIn this section, we review Bayesian decision theory (Hirschleifer and Riley;

Schimmelpfennig and Norton) and use it to develop a simple model to valueinformation provided by the USDA-led framework about impending SBR infec-tions. We also develop a set of simplifying assumptions to derive a scalar indexof information accuracy (Lawrence).

We begin by characterizing the problem in terms of a payoff matrix that mapsa finite set of possible farmer actions x ∈ {x1, x2, . . . , xX} and a finite set of mutu-ally exclusive states s ∈ {s1, s2, . . . , sS} to an X × S matrix of possible outcomes,the elements of which are denoted by px,s. The unconditional probability thatany given state s will occur is �s. These probabilities are subjective: they per-tain to a farmer’s beliefs about the chances that each state will occur, and weassume these beliefs are consistent with the laws of probability (all �s ≥ 0 and�s�s = 1).

An information signal is modeled as a random variable M, which might realizeoutcomes such as mL, signaling “low risk of infestation,” or mH, signaling a “highrisk of infestation.” In general, there may be any number of possible messages. Themessage is valuable if it arrives before the farmer chooses an action and causes thefarmer to change beliefs about the probability that states s will occur. The posteriorprobability, the probability of s given M (�sM), is linked to the prior probability(�s) using Bayes rule

�s, M = Pr[s | M] = �sPr[M | s]

Pr[M].(1)

The quality of the information signal depends on the magnitude of the differ-ence between �sM and �s. A perfect information signal would cause a completeresolution of uncertainty, so that if the state s∗ ultimately arises, �s∗M = 1 and�−s∗M = 0. Thus, for perfect information, the number of possible outcomes fromthe message M must equal the number of possible states S, and the distributionof M must be identical to the distribution defined by the probabilities �s. That is,Pr[M = s] = �s and Pr[s = M | M] = 1. For example, if there are two states of theworld, “infestation” and “no infestation,” then analogous messages that forecast“impending infestation” or “no impending infestation” would occur with the


same frequency as infestations themselves (Pr[M = s] = �s), and the messageswould always be correct (Pr[s = M | M] = 1).

The more realistic and interesting case is when information is imperfect. Ingeneral, the number of possible messages may be greater than, less than or equalto the number of possible states, and both the conditional and unconditionalprobability distributions of messages can take many forms. One way to simplifythe issue is to assume the message is a forecast that predicts which state willoccur, and that the unconditional probability distribution of messages equals theprobability distribution of states. Hence, as in the case of perfect information,Pr[M = s] = �s. We therefore define the unconditional probability density functionof M using the same notation as the states, e.g., �M. Unlike the case of perfectinformation, however, Pr[s = M | M] < 1; that is, it is anticipated that the forecastmay be inaccurate. From Bayes rule, we can see that in this special case

�s M = Pr[s | M] = Pr[M | s] = Pr[M ∩ s]�s

.(2)

By simplifying the problem in this way, we can model information quality usinga single index of message accuracy � ∈ (0, 1), where information quality tends tozero as � tends to 0 and information quality tends to perfect accuracy as � tendsto 1. We do this by setting

Pr[M ∩ s] = �s�M + �(1 − �s�M).(3)

This expression implies that M and s are independent when � = 0 (the mes-sage contains no information) and perfectly correlated (Pr[M ∩ s] = �s) when� = 1 (perfect information). The expression in (3) is simply a linear interpola-tion between these two extremes. Under this set of assumptions, the posteriordistribution is linked to the prior distribution by

�s M = �s�M + �(1 − �s�M)�s

.(4)

The value of information depends on the effect the message has on the decisionsfarmers make. Without a message, farmers maximize expected profit given theirprior beliefs, �s. We denote these actions by x∗. With information, farmers choosetheir actions to maximize expected profits conditional on the message M. Wedenote these actions by x∗ | M. Payoffs are given by the combination of the statethat occurs and action chosen and denoted pxs. Taking expectations, the ex antevalue of information given by message M is therefore

VOI =∑

M

∑

s

�s M psx∗ | M −∑

s

�s psx∗ .(5)

Estimating the Value of the SBR Monitoring FrameworkTo estimate the value of the SBR monitoring framework we must delineate farm-

ers’ possible management strategies (actions) and possible payoffs. We assume


Figure 1. Decision tree without information about soybean rustinfection

Infest(prob=π)

SBR

PREVENTDECISION

NoInfest

Monitor

NoApply

Payoff(5.)

Payoff(1.)

Payoff(2.)

Apply

SBR SBR

Apply Curative

CUREDECISION

CUREDECISION

Payoff(3.)

Payoff(4.)

NoCurative

Infest(prob= π)

NoInfest

Infest(prob= π)

NoInfest

Payoff(6.)

Notes: Square boxes indicate farmers’ decisions and the circles represent nature’s random decisionwhether or not to infest. The payoffs (1–6) are described in table 1.

Table 1. Possible outcomes stemming from P. pachyrhizi threat

Management Strategy Infection No Infection

Apply preventive treatment 1 21% yield loss, cost of $25.63/acre Cost of $25.63/acre

Monitor fields and apply 3 4curative treatment if SBR 7% yield loss, cost of $20.52/acre Cost of $6.71/acre

No rust management 5 625% yield loss Base return

Source: Johansson et al.

three management strategies: (a) apply a preventive fungicide before soybean rustoccurs; (b) intensively monitor fields and apply a curative fungicide if soybeanrust is detected; or (c) do nothing. The payoffs and profit-maximizing strategiesdepend on the costs of preventive and curative fungicides, monitoring costs,expected yield losses in the event of an infection, soybean prices, and farmers’perceptions of the probability that infection will occur. The decision tree in figure 1shows how the three strategies, crossed with two possible states (infestation andno infestation), lead to six possible payoffs, which are summarized in table 1.2

The costs in this table are treatment cost, not the cost of the yield loss.


Figure 2. Decision tree with partial information about soybean rustinfection

Infest(prob= H)

SBR

PREVENTDECISION

NoInfest

Monitor

No Apply

Payoff(5.)

Payoff(1.)

Payoff(6.)

Payoff(2.)

Apply

SBR SBR

CUREDECISION

CUREDECISION

‘‘High Risk’’signal

(prob=π)

‘‘Low Risk’’signal

(prob=1-π)

INFO

PREVENTDECISION

Monitor

No Apply

Apply

Infest(prob=

SBR

NoInfest

Payoff(5.)

Payoff(1.)

Payoff(6.)

Payoff(2.)

SBR SBR

CUREDECISION

CUREDECISION

Apply Curative

Payoff(3.)

Payoff(4.)

NoCurative

Apply Curative

Payoff(3.)

Payoff(4.)

NoCurative

Infest(prob=

NoInfest

Infest(prob=

NoInfest

Infest(prob=

NoInfest

Infest

NoInfest

Notes: Square boxes indicate farmers’ decisions and the circles represent nature’s random decisionsabout the information signal and whether or not to infest. The payoffs (1–6) are described in table 1.

Figure 2 illustrates the decision tree for an environment with an imperfectinformation signal. In this environment, management decisions are made afterreceiving an information signal, M, which changes farmers’ beliefs about infec-tion from the prior, � to posterior �H or �L, depending on whether it is a “high-”or “low-risk” signal. The accuracy of the signal, �, ranges continuously between0 and 1: the higher is �, the more the signal changes farmers’ beliefs. If infor-mation quality were perfect, we would expect only two signals, one perfectlyforecasting an impending arrival of SBR and one perfectly forecasting the nonar-rival of SBR—that is, �H would equal 1 and �L would equal zero. To approx-imate a continuum of information qualities, we suppose there remain just twosignals, but that the signal itself may have different levels of accuracy. If neitherof the two signals contained informational content, they would not alter farmers’priors (� = �H = �L), and farmers would choose the same management strat-egy in the partial information environment as they would in the no-informationenvironment.

Because we do not have objective estimates for information accuracy, we eval-uate farmers’ optimal conditional strategies and expected profits over a range ofaccuracies: � = 0.2 (low), � = 0.5 (medium), and � = 0.8 (high). One may think ofthese information qualities as the proportion of uncertainty resolved by the partialinformation. We then calculate farmers’ overall expected profits by multiplyingconditional expected profits by the probability of each signal and summing them,as per equation (5).


Quantifying Payoffs and Probabilities

Soybean Yield ImpactsFungicide efficacy trials from Brazil and Paraguay in 2001–2003, aggregate

yield data for 10 Brazilian states during 1993–2002, and data on the introduc-tion of P. pachyrhizi into those states were used to estimate rust-free yields andtreated and untreated yield impacts (Livingston et al.). Rust-free yields aver-aged 2.604 (±0.422) metric tons per hectare, and treated and untreated yieldsaveraged 2.578 (±0.201) and 2.025 (±0.363) metric tons per hectare. Estimatedtreated and untreated yields were therefore lower by an average 4.3% (±5.2%) and25.0% (±11.9%), respectively, than estimated rust-free yields.

We use the untreated yield impacts to estimate payoffs when rust occurs butno fungicide is applied. Because the treated yield impacts were estimated withyield data reported from soybean plots sprayed with curative, preventive, orcurative plus preventive fungicides, we must separate impacts of the differentkinds of treatments. Replicating the methods in Johansson et al., we find that theaverage yield impact for the preventive class of fungicides is −0.97%. The averageyield impact for the curative class of fungicides is −6.95% with a mean of 1.39applications evaluated (see table 2 and Livingston et al.).3

Prior Infection ProbabilitiesWe develop regional proxies for prior probabilities of SBR infestations using

data on wheat stem rust, a disease that spreads through the air much like SBR.Stem rust epidemics of wheat for 1921–62 (Hamilton and Stakman) are used toestimate how often P. pachyrhizi spores may be present in most states where soy-beans are produced (U.S. Department of Agriculture, 2005). We also use dataon daily temperature extremes, rainfall, and humidity for 1992–2001 to estimatethe proportion of years in which conditions may favor the development of soy-bean rust in each state (Livingston et al.). P. pachyrhizi may be able to overwinteralong the coastlines of Alabama, Florida, Georgia, Louisiana, Mississippi, andTexas (Pivonia and Yang); therefore, we assume that climatic conditions will fa-vor introduction of soybean rust in all years for these states. In addition, becauseP. pachyrhizi is an obligate parasite that can not live without a host plant, we usedata on the most likely soybean planting and harvesting dates for each state (U.S.Department of Agriculture, 1997) to estimate how often climatic conditions andhost availability may favor rust epidemics.

To estimate state-level prior probabilities for rust infections, we use the productof the proportion of years that stem rust epidemics actually occurred and the pro-portion of years that climates favored the spread of rust. This assumes climaticconditions affecting the dispersal of spores and those affecting the broader estab-lishment of rust in an area are independent (Hamilton and Stakman). To convertstate-level prior probabilities to regional probabilities, we weight states by aver-age 1995–2004 soybean production (U.S. Department of Agriculture, 1998–2005).Over all U.S. soybean acres, these calculations imply an average prior probabilityof rust infection equal to 0.53. Across regions, the priors are 0.67, 0.55, 0.55, 0.49,0.62, 0.43, 0.76, and 0.51 for Appalachia, Corn Belt, Delta, Lake States, North-east, Northern Plains, Southeast, and the Southern Plains, respectively.4 These


Table 2. Yields with preventive and curative fungicides

Rust-Free Efficacy Preventive CurativeYield Estimate Trial Yield Yield Treatments Yield Treatments(Tons/Acres) (Tons/Acres) Impact (%) (Number) Impact (%) (Number) Source

2.223 1.914 −14 2 a2.223 1.765 −21 22.223 1.776 −20 2

2.549 2.149 −16 2 b2.549 2.190 −14 22.549 2.090 −18 22.549 1.832 −28 2

2.549 2.767 9 1 c2.549 2.946 16 12.549 2.548 0% 12.549 2.712 6% 1

2.549 2.926 15 1 d

3.359 3.969 18% 1 e3.359 3.641 8% 13.359 3.813 14% 13.359 3.531 5 13.359 3.656 9 13.359 3.313 −1% 13.359 3.375 0% 13.359 2.938 −13% 13.359 2.984 −11% 13.359 2.703 −20 13.359 3.313 −1 13.359 3.250 −3% 13.359 3.328 −1% 13.359 2.984 −11 13.359 3.203 −5 1

2.750 2.469 −10% 1 f2.750 2.516 −9% 12.750 2.406 −13% 12.750 2.578 −6 12.750 2.625 −5 1

2.686 2.568 −0.97% 1.00 −6.95 1.39 Mean

Source: (a) Bayer (2003a) (Trials 1 and 2). Lower bound of rust-free yield estimate for Mato Grassodo Sul 2001–02. (b) Bayer (2003b) (Trial 14). The estimate for rust-free yield in Minas Gerais 2002–03.(c) Bayer (2003b) (Trial 15). The estimate for rust-free yield in Minas Gerais 2002–03. (d) Bayer(2003b) (Trial 16). The estimate for rust-free yield in Minas Gerais 2002–03. (e) BASF (2003) (Jesus,Paraguay). The upper bound of the rust-free yield estimate for Parana 2002–03. (f) BASF (2003)(Pirapo, Paraguay). The estimate for rust-free yield in Mato Grasso do Sul 2002–03.Note: Blank fields indicate no data: Each study considers either preventive or curative fungicidetreatments.

probabilities are used to estimate information values in the base case (table 3) andother scenarios.

Our rather high estimated priors may appear inconsistent with the actual U.S.SBR experience after 2005 since SBR has not yet posed a serious threat to theoverall U.S. soybean crop. It is possible, however, that our estimated infestation


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rates continue to be reasonable, even after 2005 when U.S. farmers had not anyfirsthand experience with SBR. Some support for this view stems from the factthat, even following a benign year in 2005, survey data indicate many farmersremained concerned about possible SBR infection in 2006. For example, whileover 50% thought it was “very unlikely” that their fields would be infested, and22% thought it “somewhat unlikely;” there were still 6% and 3% of farmers whorespectively thought infestation was “somewhat” and “very likely” in their fields.Seventeen percent were uncertain whether their fields would be infested or not.This means over a quarter of surveyed soybean farmers thought that infestationwas more likely than not, or were uncertain. While we cannot discern preciseprobabilistic priors from qualitative survey responses, these data do indicate thatfarmers perceived significant infestation risk in 2006. Thus, it is plausible thatbeliefs were just somewhat more pessimistic a year earlier in 2005.

In 2006–2008, the actual incidence of SBR steadily increased. Plant pathologistsnow believe it will take a number of years for P. pachyrhizi spores to build upto natural equilibrium levels.5 Thus, individual-season prior infection beliefs arelikely rising again after an initial fall after the 2005 season.

Given the difficulty of determining prior beliefs of infection and the funda-mentally subjective nature of those beliefs, we supplement our base-case priorprobabilities with a sensitivity analysis that varies prior infection probabilitiesfrom 10% to 120% of our base-case estimates. We also look more closely at thesoybean-rich Corn Belt, considering for that region a continuum of prior beliefsthat ranges from zero to one.

Base Case ResultsThe value of information is the difference in expected profits between the

partial-information environment (figure 2) and the no-information environment(figure 1). Results reported in table 3 indicate that the value of information variesbetween zero and $6.01 per U.S. soybean acre, depending on information qualityand assuming prior infestation beliefs equal our estimated infestation probabili-ties. In table 4, we report information values for a whole range of priors, scaled asa percent of our estimated priors. A striking result of this sensitivity analysis is theextreme nonlinearity of the information value with respect to the prior infestationprobabilities.

To further characterize the nonlinear relationship between information valueand prior infestation beliefs, we focus on the Corn Belt region, which has thenation’s largest share of soybean production. For this region, we examine thefull range of possible priors (figure 3). Values for all three information qualitiespeak at prior infection probabilities of � = 0.19 and 0.63. These probabilities markswitching points in farmers’ optimal strategies. Below a 19% chance of infection,the best strategy is to do nothing; between a 19% and 63% chance of infection,the best strategy is monitoring and application of curative fungicides if infected;above a 63% chance of infection, the best strategy is to use preventive fungicides.For a given quality of information, values are highest near these switching points,because information has the greatest scope for altering farmers’ decisions and re-ducing the chance of ex post errors. Of course, the better the quality of information,the more ex post errors are reduced, creating greater value. When information is

314 Review of Agricultural EconomicsT

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6


Figure 3. Possible information values in the Corn Belt

Table 5. Aggregate information values for the United States

Information Quality

Low Medium High(� = 0.2) (� = 0.5) (� = 0.8)

Scenario (in Dollars) (in Dollars) (in Dollars)

Base caseU.S. total 11,247,380 132,925,747 395,277,121Average per acre 0.16 1.84 5.46

Risk aversionU.S. total 16,880,465 136,418,926 391,344,966Average per acre 0.23 1.88 5.41

Price feedbackU.S. total 28,773,280 130,259,030 376,391,350Average per acre 0.40 1.80 5.20

Heterogeneous beliefsU.S. total 16,777,090 102,300,370 275,889,857Average per acre 0.23 1.41 3.81

of low quality (� = 0.2), there are some priors for which the information providedwill not cause farmers to change their management behavior, thus producing novalue at all.

Using estimated probabilities of infection for prior beliefs in each region andaggregating on a per-acre basis across all regions, we estimate in table 5 thatthe aggregate value of information ranges between $11 million and $395 mil-lion, depending on information quality. In the next section, we show how these


information values were determined under the assumptions that farmers arestrongly risk averse, that soybean prices are influenced by soybean-rust-inducedyield losses, and farmers’ prior beliefs are heterogeneous within each region. Ascan be seen in table 5, these scenarios all increase the lowest information val-ues and reduce the highest values in comparison to the base case. Despite thebroad range of information values estimated, all far exceed the program’s esti-mated cost in the first year, which ranged between $2.5 million and $5.0 million(U.S. Department of Agriculture, 2005).6 Because the value increases between$2 million and $3 million for each percentage point of uncertainty resolved by theframework, efforts to improve timeliness and accuracy of infection forecasts maywell be cost-effective.

Alternative ScenariosIn the base case scenario described in the preceding section, we evaluate farm-

ers’ expected-profit-maximizing management decisions with and without infor-mation and estimate the value of information as the difference in expected profitsbetween the two environments. In the following scenarios, the concept is similarbut some assumptions are changed or relaxed in order to explore the sensitivityof the base-case estimates to these assumptions.

Alternative Scenario 1: Information Values of Risk-Averse FarmersWe first consider how our results change if farmers are strongly risk averse.

More specifically, we assume farmers’ preferences can be characterized by con-stant relative risk aversion (CRRA), with a coefficient of relative risk aversionequal to 4. This may be expressed with the utility function: u(W) = −AW−3/3,where W indicates wealth, and A is an arbitrary constant. We made this assump-tion to throw into stark relief the effect of risk aversion on information values.

Using data from USDA’s 2003 Agricultural Resource Management Survey, weestimate base wealth for each region by weighting farm households’ net worthby their number of soybean acres. We find that wealth varies considerably acrossfarm sizes and across the country, with the average soybean acre being associ-ated with a household net worth of $1,649,807 in Appalachia and $1,348,667 inthe Corn Belt, but only $918,870 in Delta states. Average net worth is $1,430,615in Lake States, $1,030,815 in the Northeast, $1,389,427 in the Northern Plains,$1,300,438 in the Southeast, and $1,572,391 in the Southern Plains. Net worth forthe average soybean acre of farms outside these regions is $915,964. Calculatinginformation values for risk-averse farmers’ proceeds similarly to the base casedescribed earlier, except that farmers are assumed to maximize expected utilityrather than expected profits.

In only a few cases does the extreme level of risk aversion cause farmers’ deci-sions to differ from the base case. This assumption changes information values,however, mainly because different information environments may lead to largedifferences in profit variability. For example, consider a farmer who would haveapplied the preventive strategy without information. Suppose that if armed witha high-quality forecast, the farmer chooses prevention in response to a “high-risk” signal and does nothing in response to “low risk.” The information wouldcause her average profits to increase but would also cause her profit variability to


increase, so the information would be valued less by this farmer than by anotherwho is less risk-averse. When the information signal is of poorer quality, informa-tion may increase or decrease the amount of risk, so the information value maybe relatively greater or smaller than in the risk-neutral base case.

Table 6 reports results from the analysis of risk-averse farmers. Differences fromthe base-case scenario are generally modest and vary somewhat across regionsand information qualities. In the Corn Belt, for example, a strongly risk-aversefarmer values low-quality information at $0.37 per acre versus the base-case valueof $0.22. Alternatively, the same risk-averse farmer values high-quality informa-tion at $5.96 per acre, which is slightly less than the value of $6.01 in the base case.More realistic assumptions about the level of risk aversion would imply smallerdifferences from the base case.7 U.S. aggregate information values (see table 5)range from almost $17 million (low quality) to over $391 million (high quality).

Alternative Scenario 2: Price Feedback EffectsThe base case scenario assumed soybean prices were fixed at the May 2, 2005,

futures price. However, both economic theory and historical evidence indicatethat soybean prices vary with yield, and because each decision (prevent, moni-tor/cure, or no management) and each outcome (rust infection or no rust infection)leads to different yields, we consider the additional possibility that postharvestsoybean prices are endogenous. Table 7 presents information values similar tothose in table 3, except infestations and farm management decisions are assumedto influence market prices for soybeans.

Equilibrium soybean price is determined as follows: individual farmers, takingexpected postharvest price as given, maximize their own profits, while the indus-try as a whole, which is made up of these individual profit-maximizing farmers,satisfies one of the equations below. In these equilibrium equations, the May 2futures price equals the average of all potential end-of-season soybean prices,weighted by the market-perceived probabilities that these prices will be realized.In the case where no information is available, this means:

Prob(RUST infection) × (Post-harvest price w/RUST infection)

+ Prob(no infection) × (Post-harvest price w/o infection) = Futures price.

(6)

With partial information, this condition becomes:

Prob(infection and “high risk” signal)

× (Post-harvest price w/infection and “high risk” signal)

+ Prob(infection and “low risk” signal)

× (Post-harvest price w/infection and “low risk” signal)+ Prob(no infection) × (Post-harvest price w/o infection) = Futures price.

(7)

The above conditions are only correct if the geography of the soybean marketcoincides with that of the SBR infection and message probabilities. Given the widevariation in climate conditions across the United States and the global nature of


Tab

le6.

Info

rmat

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valu

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ith

risk

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sion

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Hig

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Val

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ase

No

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No

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kR

isk

EU

Wit

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fect

ion

Wea

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ion

(Pro

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(P,M

,or

N)

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to1)

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,or

N)

(P,M

,or

N)

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0.67

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354

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8P

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551,

348,

667

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0.37

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1,34

8,66

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Tab

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Con

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ued

Pri

orC

Eof

Hig

hL

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Eof

Val

ue

ofV

alu

eof

Bel

ief

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No

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EU

No

Info

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Ris

kR

isk

EU

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hIn

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lth

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300,

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dut

ility

”an

dC

Ein

dic

ates

“cer

tain

tyeq

uiva

lenc

e,”

whi

chis

the

cert

ain

leve

lofp

rofit

sw

ith

sam

eut

ility

asth

eac

tual

,unc

erta

inle

velo

fpro

fits.


Tab

le7.

Info

rmat

ion

valu

esw

ith

pri

ceef

fect

s

Pri

orH

igh

Low

Low

Val

ue

ofV

alu

eof

Bel

ief

ofN

oIn

foE

VN

oIn

form

atio

nR

isk

Ris

kR

isk

EV

Wit

hIn

foP

erIn

foP

erIn

fect

ion

Dec

isio

nIn

foQ

ual

ity

(�)

Dec

isio

nD

ecis

ion

EV

Info

Farm

Acr

eR

egio

n(P

rob

abil

ity)

(P,M

,or

N)

(Dol

lars

)(S

cale

0to

1)(P

,M,o

rN

)(P

,M,o

rN

)(D

olla

rs)

(Dol

lars

)(D

olla

rs)

(Dol

lars

)

App

alac

hia

0.67

M78

,519

0.2

PM

84,5

3379

,442

923

0.83

0.67

M78

,519

0.5

PM

90,0

7081

,174

2,65

52.

370.

67M

78,5

190.

8P

N10

0,50

784

,540

6,02

15.

39C

orn

Bel

t0.

55M

93,3

020.

2P

M99

,471

93,8

1951

70.

700.

55M

93,3

020.

5P

M10

1,72

295

,424

2,12

12.

860.

55M

93,3

020.

8P

N10

7,54

797

,568

4,26

55.

75D

elta

0.55

M98

,203

0.2

MM

104,

540

98,2

030

00.

55M

98,2

030.

5P

N11

2,91

499

,763

1,56

00.

800.

55M

98,2

030.

8P

N12

9,99

610

6,85

98,

657

4.43

Lak

eSt

ates

0.49

M58

,608

0.2

MM

59,9

4558

,608

00

0.49

M58

,608

0.5

PM

62,8

2659

,217

610

1.14

0.49

M58

,608

0.8

PN

67,1

0861

,239

2,63

24.

93N

orth

east

0.62

M41

,936

0.2

PM

45,3

0742

,216

279

0.59

0.62

M41

,936

0.5

PM

47,1

9243

,152

1,21

62.

570.

62M

41,9

360.

8P

N51

,267

44,4

812,

545

5.38

Con

tinu

ed


Tab

le7.

Con

tin

ued P

rior

Hig

hL

owL

owV

alu

eof

Val

ue

ofB

elie

fof

No

Info

EV

No

Info

rmat

ion

Ris

kR

isk

Ris

kE

VW

ith

Info

Per

Info

Per

Infe

ctio

nD

ecis

ion

Info

Qu

alit

y(�

)D

ecis

ion

Dec

isio

nE

VIn

foFa

rmA

cre

Reg

ion

(Pro

bab

ilit

y)(P

,M,o

rN

)(D

olla

rs)

(Sca

le0

to1)

(P,M

,or

N)

(P,M

,or

N)

(Dol

lars

)(D

olla

rs)

(Dol

lars

)(D

olla

rs)

Nor

ther

nPl

ains

0.43

M70

,621

0.2

MM

72,0

3270

,621

00

0.43

M70

,621

0.5

PM

/N

77,8

0470

,588

(33)

(0.0

4)0.

43M

70,6

210.

8P

N83

,612

74,5

513,

930

4.47

Sout

heas

t0.

76M

2,41

90.

2M

M3,

997

2,41

90

00.

76M

2,41

90.

5P

N7,

570

3,03

761

81.

390.

76M

2,41

90.

8P

N11

,239

3,96

21,

543

3.48

Sout

hern

Plai

ns0.

51M

24,8

070.

2M

M/

N30

,006

24,7

03(1

03)

(0.0

7)0.

51M

24,8

070.

5M

N38

,578

26,6

051,

798

1.18

0.51

M24

,807

0.8

PN

48,7

8730

,456

5,64

93.

71O

ther

0.53

M69

,085

0.2

MM

72,4

8169

,267

00

0.53

M69

,085

0.5

PN

78,1

6270

,097

830

0.76

0.53

M69

,085

0.8

PN

86,8

8474

,039

4,77

24.

35

Not

es:I

nth

ed

ecis

ion

colu

mns

,Mis

mon

itor

/cu

re,P

ispr

even

t,an

dN

isd

ono

thin

g.In

colu

mn

head

ings

,EV

ind

icat

esex

pect

edva

lue.


the soybean market, this is unrealistic. Allowing probabilities to vary by location,however, quickly renders the price equilibrium condition intractable. Even withthe simplifying assumption that infection and message probabilities are homoge-neous within each of the eight major soybean-producing regions,8 the number ofterms on the left-hand side of the partial information equilibrium equation climbsto 6,561. After all, there are three yield-determining outcomes (“high risk” mes-sage with infection, “low risk” message with infection, and no infection) possiblein each region, producing 38 characterizations for the nation as a whole.

Though we do not explicitly model the regional interconnectedness that pro-duces this host of outcomes, we allow for such effects by not including alternatelocation yield shocks as explanatory variables in our regressions of postharvestsoybean price on regional yields (there are eight regressions—one for each region).Thus, our coefficient estimates will capture not only the effect of a specific region’syield on postharvest soybean price but also the effects of other yield shocks thatare correlated with the region’s own yield shocks (presumably those occurringin locations close in distance and weather). While these estimates provide someinsight into how regional soybean prices and yields have been spatially correlatedhistorically, there is no guarantee soybean rust will exhibit similar spatial effectsas the weather and production shocks of the past decades. If, for example, soy-bean rust were to spread quickly over the entire soybean-producing part of NorthAmerica, a rust-induced regional price increase would likely be greater than theincrease resulting from yield loss caused by a more localized drought.

Our first step is to aggregate, using production-weighted averages, state-leveldata (U.S. Department of Agriculture 1950–2004) to the regional level. Next, inorder to abstract from yearly variations in output while still accounting for pro-ductivity increases over time, we fit a smooth trend curve for yields in all ninesoybean production regions. Examples of these trends for the Corn Belt and South-east are given in figure 4.

Figure 4. Yield trends and shocks in the Corn Belt and Southeast

1950 1960 1970 1980 1990 2000

2530

3540

45

Corn Belt Yields and Yield Trend, 1950-2004

Year

Yie

ld (

bush

els/

acre

)

1950 1960 1970 1980 1990 2000

1618

2022

24

Southeast Yields and Yield Trend, 1950-2004

Year

Yie

ld (

bush

els/

acre

)


This fitting process allows us to calculate, for each region in each year, a percent-age residual yield (i.e., the difference between actual yield and yield predictedby the trend, divided by the yield predicted by the trend). We approximate thepercentage change in regional soybean prices by calculating the year-to-year dif-ference in the natural logarithm of the real price. By regressing this value on thepercentage residual yield, we obtain an estimate of the percentage change in pricethat would result from a percentage deviation from the yield trend.9, 10

In computing the results in table 7, we first find the equilibria11 in which allfarmers within a region make identical management decisions. In just two cases,such equilibria do not exist: the Northern Plains with an information quality of0.5 and the Southern Plains with an information quality of 0.2. For these regions,we consider equilibria where farmers apply one strategy to a share of acreagewithin a region and apply another strategy to the remainder. In these two cases,in equilibrium, farmers are indifferent between monitoring and no-managementstrategies when they receive the low-risk signal. An equilibrium results in theNorthern Plains scenario when, in response to a low-risk signal, about 35% ofacreage is monitored, the remainder is unmanaged, and the postharvest price,when the signal indicates low risk but infection occurs anyway, is $6.91. Similarly,the Southern Plains is in equilibrium when, in the face of low risk, about 27% ofacreage is monitored; 73% is unmanaged; and the postharvest price, when thesignal indicates a low risk-signal but infection occurs anyway, is $6.45.

For most regions, accounting for price effects has a small influence on informa-tion values. The effect is somewhat greater in the Corn Belt and Northern Plains

Figure 5. Density of farmers’ heterogeneous prior beliefs in the CornBelt


Tab

le8.

Info

rmat

ion

valu

esw

ith

het

erog

eneo

us

pri

orb

elie

fs

Ave

rage

Ave

rage

Ave

rage

Pri

or“a

lph

a”“b

eta”

Val

ue

ofV

alu

eof

Bel

ief

ofP

aram

eter

Par

amet

erN

oIn

foE

VN

oIn

form

atio

nIn

foP

erIn

foP

erIn

fect

ion

for

Bet

afo

rB

eta

Dec

isio

nIn

foQ

ual

ity

(�)

Farm

Acr

eR

egio

n(P

rob

abil

ity)

Pri

orP

rior

(P,M

,or

N)

(Dol

lars

)(S

cale

0to

1)(D

olla

rs)

(Dol

lars

)

App

alac

hia

0.67

2.00

1.00

M78

,644

0.2

239

0.21

0.67

2.00

1.00

M78

,644

0.5

1,46

51.

310.

672.

001.

00M

78,6

440.

83,

957

3.54

Cor

nB

elt

0.55

1.20

1.00

M93

,707

0.2

182

0.25

0.55

1.20

1.00

M93

,707

0.5

1,13

21.

530.

551.

201.

00M

93,7

070.

83,

001

4.04

Del

ta0.

551.

201.

00M

97,9

630.

239

10.

200.

551.

201.

00M

97,9

630.

52,

360

1.21

0.55

1.20

1.00

M97

,963

0.8

6,50

43.

33L

ake

Stat

es0.

490.

951.

00M

58,5

730.

213

70.

260.

490.

951.

00M

58,5

730.

580

11.

500.

490.

951.

00M

58,5

730.

82,

185

4.09

Nor

thea

st0.

621.

601.

00M

42,1

090.

210

70.

230.

621.

601.

00M

42,1

090.

566

01.

390.

621.

601.

00M

42,1

090.

81,

793

3.79

Con

tinu

ed


Tab

le8.

Con

tin

ued

Ave

rage

Ave

rage

Ave

rage

Pri

or“a

lph

a”“b

eta”

Val

ue

ofV

alu

eof

Bel

ief

ofP

aram

eter

Par

amet

erN

oIn

foE

VN

oIn

form

atio

nIn

foP

erIn

foP

erIn

fect

ion

for

Bet

afo

rB

eta

Dec

isio

nIn

foQ

ual

ity

(�)

Farm

Acr

eR

egio

n(P

rob

abil

ity)

Pri

orP

rior

(P,M

,or

N)

(Dol

lars

)(S

cale

0to

1)(D

olla

rs)

(Dol

lars

)

Nor

ther

nPl

ains

0.43

0.75

1.00

M70

,688

0.2

179

0.20

0.43

0.75

1.00

M70

,688

0.5

1,07

71.

220.

430.

751.

00M

70,6

880.

83,

009

3.42

Sout

heas

t0.

763.

201.

00M

2,40

80.

281

0.18

0.76

3.20

1.00

M2,

408

0.5

450

1.01

0.76

3.20

1.00

M2,

408

0.8

1,11

12.

51So

uthe

rnPl

ains

0.51

1.05

1.00

M24

,973

0.2

243

0.16

0.51

1.05

1.00

M24

,973

0.5

1,46

50.

960.

511.

051.

00M

24,9

730.

83,

734

2.45

Oth

er0.

531.

131.

00M

69,1

590.

223

40.

210.

531.

131.

00M

69,1

590.

51,

396

1.27

0.53

1.13

1.00

M69

,159

0.8

3,84

63.

51

Not

es:

Inth

ed

ecis

ion

colu

mn,

Mis

mon

itor

/cu

re.

Inot

her

colu

mn

head

ings

,E

Vis

expe

cted

valu

e,an

d“a

lpha

”an

d“b

eta”

para

met

ers

are

thos

ein

the

beta

prob

abili

tyd

istr

ibut

ion.


because yield shocks in these soybean-intensive regions have larger estimatedprice effects. In the Corn Belt, for example, the value of information increasesfrom the table 3 amount of $0.22 per acre to $0.70 per acre when it is of low qualityand declines from $6.01 to $5.75 when it is of high quality. In the Southeast, wherethe estimated price effects are far smaller, the values of both low- and high-qualityinformation are unchanged at zero and $3.48 per acre, respectively.

When we account for price feedback effects, small changes in expected yieldlead to small changes in expected price (i.e., the futures price). If informationcauses an increase in expected yield, expected prices tend to decline. If the ex-pected price decline is large enough, farmers’ total expected profits might de-cline because of the information, even though individual farmers find the infor-mation valuable (because individual farmers take prices as given). For soybeanconsumers, however, this price decline is a gain—it represents a transfer fromproducers to consumers. Of course, the opposite is true if the information causesa decline in expected yield: prices increase, and consumers experience a welfareloss because of the information’s existence

Alternative Scenario 3: Average Information Values for Farmswith Heterogeneous Beliefs

A third departure from the base case results comes from changing our assump-tions about farmers’ prior beliefs. Whereas in the base case we assume all farmerswithin a region hold the same prior beliefs about the probability of infection, inthis scenario we assume farmers have heterogeneous prior beliefs. Specifically,we assume beliefs within a region are distributed according to a beta distributionwith the beta parameter equal to one and the alpha parameter set so that the meanequals the prior probability of infection in the base case (table 3). This assumptionimplies that farmers’ beliefs vary widely within each region.

The assumed distribution for the Corn Belt is plotted in figure 5. The height ofthe density curve shows the relative proportion of farmers assumed to have theprior belief plotted along the horizontal axis. We estimate average informationvalues for each region and information quality by taking 1,000 random draws fromthe assumed beta distribution, using each draw as the value for P, calculating theassociated information values from each draw, and then taking the average of theinformation values across all 1,000 draws (table 8).

In general, heterogeneous prior beliefs tend to reduce the highest informationvalues and increase the lowest ones. The highest values decline because theyare associated with the highest-value prior beliefs—those near the critical prob-abilities that mark the switching points between strategies. With heterogeneousbeliefs, these high-value prior beliefs are averaged with lower value prior beliefs,bringing down the overall average. Conversely, the lowest value prior beliefs areaveraged with higher value prior beliefs, which bring those information valuesup.

ConclusionThe value of disease information to farmers depends on many factors, but par-

ticularly their perceived risk of being infected with SBR at the beginning of theseason and the accuracy of forecasts provided by the program. Over a broad range


of plausible parameters, the value of information provided by the SBR Coordi-nated Framework could have been substantial even though the disease did notspread to the major soybean growing regions in the Midwest. If the forecasts werepoor, resolving only 20% of SBR infection uncertainty for all fields planted withsoybeans, the estimated value of the program was $11 million during the first year.If the forecasts resolved 80% of infestation uncertainty, the estimated value was$395 million. The estimated value is also sensitive to prior beliefs about the likeli-hood of infestation. Unlike forecast accuracy, however, the relationship betweeninformation value and prior beliefs is highly nonlinear. While some alternativeprior beliefs would lead to lower information values as compared to our baseline,others give much higher values.

The sensitivity of information value to the extent of resolved uncertainty sug-gests that the potential value of information will be greatest for pest problemsthat can be forecasted accurately, that farmers have little experience with, andthat have large potential impacts on crop production that can be mitigated usingpreventive management activities (Carlson). Other key drivers of the total valueof information are the size and value of the crop in question. For instance, the neartripling of soybean commodity prices since 2005 would imply a near tripling ofour estimated value of SBR forecasts, holding all else the same.

Two other more subtle features affect estimated information values: anticipatedprice shocks in the event of large SBR outbreaks and the risk aversion of soybeanfarmers. We find that both of these effects reduce the largest estimated values andincrease the smallest ones, but the magnitudes of these effects are modest.

By examining the value of information across a range of forecast accuracies, wehave illustrated the value of marginally improving information quality. Since themarginal information value appears large in the case of SBR, in future work it maybe worthwhile to consider models that explicitly incorporate features of the infor-mation collection system. In the SBR framework, information quality is linked tothe number of sentinel plots used for monitoring, where the plots are located spa-tially, and how frequently the sentinel plots are monitored. It would be interestingto consider the optimal mix of these policy choices. While such a model would beextremely complex, the potential social gains from its construction would seemto warrant the effort.

Such a model would need to capture the spatial and dynamic patterns of infes-tations. Our discrete two-period timing of information flows and decision makingand the way we deal with spatial dependencies are crude relative to the continu-ous and spatially dependent processes that exist in reality. In a more sophisticatedmodel, prior beliefs would be determined at different points in time for differ-ent farmers, since the timing of the growing season varies geographically. Evenwithout the monitoring framework, many farmers would have had more infor-mation thantheir beginning-of-the-season prior beliefs, say from weather reportsand news about infections further south. Thus, the relevant decision-time prior isitself uncertain at the beginning of the season. Because we found information tobe valuable across many priors, integrating over these priors would likely lead toinformation values not drastically different from the ones we have estimated. Amore sophisticated model, however, would provide insight into the appropriatestructure of information systems—where and how frequently monitoring wouldbe most valuable.


A more sophisticated model may also be able to account for the externalitiesassociated with farmers’ pest management choices. Each farmer’s monitoringand fungicide application decisions affect the likelihood that his or her neighborswill be infected. This physical externality embodies another market failure thatsits alongside the public information problem. While the optimal policy solutionwould likely involve separate tools for each problem, in practice, solving oneproblem may either mitigate or exacerbate the other.

AcknowledgmentsThe authors would like to thank two anonymous reviewers for valuable input on an earlier draft,

and the GAO for providing us data from their report (GAO-05-668R) ‘‘USDA’s Preparation for AsianSoybean Rust,’’ which was presented as a briefing for Senator Tom Harkin (Ranking DemocraticMember Committee on Agriculture, Nutrition, and Forestry) United States Senate on 28 April 2005.The authors also thank NASS for allowing us to access unpublished 2005 soybean planting intentionsdata, David Nulph and Vince Breneman for terrific GIS support, and Gabriella LaRocca for assistancewith the wheat stem rust data. The views expressed are those of the authors and should not beattributed to the Economic Research Service or the U.S. Department of Agriculture.

Endnotes1In this case study, we do not consider farmers’ planting decisions, only their fungicide application

decisions, provided they do plant. By ignoring this decision, we underestimate the value of informationprovided by the framework.

2Costs and yield losses reported in table 1 are estimates. Yield data, before and after the arrival of P.pachyrhizi are not available for the United States, nor are efficacy trial data for U.S. fungicides. Efficacydata also were not available at the time of this study for climatic regions similar to the United States.Thus, to estimate treated and untreated yield impacts of soybean rust epidemics relative to rust-freeyields, we evaluated impacts of rust on soybean yields in South America. Details are provided in anonline supplement to Roberts et al.

3Poorly timed sprays could lead to the need for additional applications (Dorrance, Draper, andHershman). We do not attempt to quantify the value of improved timing, which would likely increasethe presented estimates for the value of information.

4The regions contain the following states: Appalachia (KY, NC, TN, VA, and WV), Corn Belt (IA,IL, IN, MO, and OH), Delta (AR, LA, and MS), Lake States (MI, MN, and WI), Northeast (CT, DE, MA,MD, ME, NH, NJ, NY, PN, RI, and VT), Northern Plains (KS, ND, NE, and SD), Southeast (AL, FL,GA, and SC), and the Southern Plains (OK and TX).

5From personal communication with Douglas G. Luster, Research Leader of USDA AgriculturalResearch Service, Foreign Disease Weed Science Research Unit.

6Totals depend on which fixed, start-up costs are included. Extension agents and land-grant pro-fessors volunteered their time, which is not counted in the cost estimate. The testing labs in Beltsville,Maryland, used equipment that had already been purchased, and USDA scientists involved in severalother research projects carried out the tests.

7A farmer with this utility function and wealth of $200,000, values an additional dollar 16 times asmuch as a farmer with $400,000 and 625 times as much as a farmer with $1 million.

8Defined in “Prior Infection Probabilities” section.9Only the 20 most recent observations (1984–2004) are included in this regression.10Percentage change in price from year to year will depend not only on this year’s yield shocks, but

also on yield shocks that may have affected the previous year’s price. However, including previousyear yield residuals as an explanatory variable does not lead to significant changes in estimates of thecoefficients on current-year price-shock effects.

11The relevant equilibrium condition is expressed by equation (7).

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Econ. 52, (May 1970):216–23.Dorrance, A.E., M.A. Draper, and D.E. Hershman. Using Foliar Fungicides to Manage Soybean Rust. 2005.

Available at http://www.oznet.ksu.edu/library/plant2/MF2680.pdf.


Hamilton, L.M., and E.C. Stakman. “Time of Stem Rust Appearance on Wheat in the Western Mis-sissippi Basin in Relation to the Development of Epidemics from 1921 to 1962.” Phytopathology57(1967):609–14.

Hirshleifer, J., and J.G. Riley, The Analytics of Uncertainty and Information, Cambridge: CambridgeUniversity Press, 1992.

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Roberts, M.J., D. Schimmelpfennig, E. Ashley, and M.J. Livingston. The Value of Plant DiseaseEarly-Warning Systems: A Case Study of USDA’s Soybean Rust Coordinated Framework. Wash-ington, DC: US Department of Agriculture, Econ. Res. Rep. ERR-18, April 2006. Available athttp://www.ers.usda.gov/Publications/ERR18/.

Schimmelpfennig D.E., and G.W. Norton. “What Is the Value of Agricultural Economics Research?”Am. J. Agric. Econ., 85 (February 2003):81–94.

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