A principal-agent model for evaluating the economic value of a traceability system: a case study...

The beef supply chain consists of multiple production stages that transfer cattle and beef downstream using market transactions. Qualities, quantities, and prices are established through observation and negotiation. Market inefficiencies can occur because quality assurance efforts of upstream operations

Traceability has been proposed to reduce supply chain anonymity and information asymmetry. Improved information may more equitably allocate costs in the beef supply chain, induce preferred behavior, and compliance of suppliers, improve the quality or safety of the final beef product, and ensure that market signals are more efficiently communicated. The International Organization for Standardization (2000) states that traceability systems create the ability to retrieve the history and location of a product through a registered identity. This includes implementing computer systems and databases, identification technologies such as bar codes or tags, and improved supply chain management protocols. Antle (2001) expands this definition to include changing the production process, for example, limiting product mixing to more easily segregate output. The costs and benefits of implementing traceability depend on the breadth, depth, and precision of the traceability system (Golan et al. 2004). Breadth is the amount of information recorded, depth denotes how far forward or backward in the supply chain traceability extends, and precision represents the ability to pinpoint the source of the defect.

Previous research has examined two approaches for firms to overcome asymmetric information in supply chains: (a) to select producers based on their level of investment in product quality (overcoming adverse selection) and (b) to increase producers' efforts to improve product quality and safety by providing incentives (overcoming moral hazard).

Hennessy (1996), Chalfant et al. (1999), and Bogetoft and Olesen (2003) address the adverse selection issue. Hennessy and Chalfant et al. show that price-grade incentives are not sufficient to induce a first-best level of investment by producers if there are measurement errors in testing and grading. Bogetoft and Olesen show that these results hold only when trade occurs after grading, but do not hold when trade occurs before grading as is the case with injection-site lesions in beef products.

Dubois and Vukina (2004), Starbird (2005), and King, Backus, and Gaag (2007) use principal-agent models to evaluate the impacts of incentives offered by principals on the performance of agents. King, Backus, and Gage further show that reputation can be an added incentive mechanism to induce performance under a contract.

In the previous studies, the principal knows the agent's identity at the time an event caused by the agent is observed. This is the case when raw material is tested on delivery. However, there are many cases in which the product defect caused by the agent can be discovered only after processing has begun. By this time the identity of the raw material supplier is likely to have been separated from the processed product.

Injection-site lesions in beef cattle provide a relevant case of identity separation. Beef cattle are given injections of biological or antibiotic compounds for prevention and treatment of disease but an injection can cause a lesion when given in the muscle (Field and Taylor 2004). The incidence of injection-site lesion defects in top sirloins is at a record low of 2.5%, yet purveyors and retailers still rank them as one of the greatest quality challenges facing the U.S. beef industry (McKenna et al. 2002). In response, the National Cattlemen's Beef Association has recommended all injections, regardless of age, be moved to the neck and that injections be administered beneath the hide when allowable (Morgan, Tittor, and Lloyd 2004).

Lesions caused by injection remain concealed within the muscles and fat which makes damage observable only during portioning of the primal cuts (Roeber et al. 2001). The direct tracking of primal cuts back to an individual animal or feedlot is difficult because the packer commingles primal cuts from different carcasses to create consistent boxes of beef primal cuts (Robb and Rosa 2004).

Unlike foreign objects such as syringe needles or restricted feed additives, there is no available test to detect lesions when cattle are marketed. Therefore, it represents a case of nearly perfect information asymmetry without recourse to effective testing prior to fabrication. Though limited in overall economic importance, the technical aspects of injection-site lesions are well documented and provide the necessary technical data for a numerical economic analysis.

Our objective is to develop a principal-agent game structure to identify optimal levels of traceability investment to overcome information asymmetry and to quantify incentive mechanisms necessary to induce first-best behavior on the part of risk-averse agents. To examine the economic costs of asymmetric information, a benchmark scenario wherein the information is symmetric and two scenarios with information asymmetry and the inclusion of traceability are developed and simulated using the case of injection-site lesions. This extends previous research in principal-agent modeling by developing a numerical solution parameterized by the technical information on injection-site lesions in beef.

The Principal-Agent Game

A hypothetical meat packer (principal) purchases live animals from a group of N homogeneous cattle feeders (agents) to run a one-time project. Prior to this transaction, the cattle feeder gives injections by a method that affects the frequency and type of injection-site lesions in beef retail cuts. Three methods, [a.sub.i], comprise the action space, A = (give all injections in the rear leg ([a.sub.1]), give all injections in the neck area ([a.sub.2]), and give all injections with a needle-free technique ([a.sub.3])). Giving injections in the rear leg can result in lesions in the highest-valued cuts of the animal, while giving injections in the neck area can result in lesions in lower-valued cuts. The needle-free injection method is most costly to implement, but is assumed to produce no lesions (Morgan, Tittor, and Lloyd 2004). The cattle feeder could choose not to give any injection. However, the expected losses from animal diseases are assumed to be higher than the costs of adopting a needle-free technique, so that the cattle feeder's best practice is to always give injections as required for animal health. The packer cannot verify the method of injection used by the cattle feeder at the time the cattle are marketed.

A traceability system described by Basarab, Milligan, and Thorlakson (1997) is assumed to be added from the slaughter floor to the fabrication floor in a typical beef packing plant to help make the link between a beef cut and the cattle feeder. The system employs radio frequency identification, database management of products and flows, and sequential processing methods to maintain the identity of beef cuts to their origin.

Failures are expected to occur due to hardware and software breakdown and incompatibility, plant logistics, and electromagnetic interferences with the radio frequency identification readers. The traceability system is fully characterized by t, the probability of successfully identifying a cattle feeder and animal with a specific retail beef cut. Experiments conducted and reported by Basarab, Milligan, and Thorlakson (1997) are used to set the traceback success rate for three traceability systems as t [member of] T = (38.9%, 43.7%, and 95 %).

[FIGURE 1 OMITTED]

Given the premises that cattle feeders' injection actions can cause lesions and that the beef packer employs a traceability system, the two-stage sequential game with complete and perfect information runs as shown in figure 1.

A game with complete and perfect information implies that players' payoffs are common knowledge and that players know the full history of the game by the time of their move (Gibbons 1992, p. 55). So, by the time an injection decision is made, the feeder knows the traceability system's reliability and the contingent payment scheme set in the game's first stage.

The Packer's Cost Minimization Function

To formulate the packer's cost minimization problem, every injection-site lesion event and its probability of occurrence must be identified. The variable [P.sub.l,(j)] represents the probability of each one of the sixteen possible combinations of injection-site lesion events: eight for if traceability is successful (l = 1), and eight for if it is not successful (l = 0). The packer can identify the cattle feeder responsible for the lesion only if traceback is successful. Subscript j identifies the type of lesion or combination of lesions found in each carcass side ("c" for chuck steak lesion, "r" for round steak lesion, "s" for sirloin steak lesion, and "0" for no lesion). For example, [P.sub.1,0] is the probability that the traceability system works and no lesion is observed. Similarly, if the traceability system works and at least one lesion is observed in the chuck, round, and sirloin, then the probability of this event is represented as [P.sub.1,(c,r,s)]. The probability that the traceability system fails to work, [P.sub.0*], is the sum of each injection-site lesion event probability. Alternatively, [P.sub.0*], can be calculated as (1 - t).

The occurrence and type of injection-site lesion depends on the method of injection, [a.sub.i], used by the cattle feeder. The underlying probability that at least one lesion is observed in a chuck cut, a bottom-round cut, or a top sirloin cut is denoted by [F.sub.c]([a.sub.i]), [F.sub.r]([a.sub.i]), and [F.sub.s]([a.sub.i]). Hence, the probability that the traceability system works and at least one lesion is observed in the chuck, the round, and the sirloin is defined as [P.sub.1,(c,r,s)] = t[F.sub.c]([a.sub.i])[F.sub.r]([a.sub.i])[F.sub.s]([a.sub.i]). All the other event probabilities in the model are calculated in this same fashion.

The packer (principal) makes an income transfer [I.sub.l,(j)] to a cattle feeder (agent) as payment for the cattle. For l = 0 the traceability system fails to work and the income transfer ([I.sub.0*]) is made to the cattle feeder regardless of the presence of a lesion. For l = 1, the traceability system works and now the packer can make the adjusted income transfer ([I.sub.1,(j)]) to the cattle feeder contingent on the combination of lesions found.

The packer's objective is to minimize the costs of procuring the cattle subject to the costs and incidence of lesions. Objective function (1) reflects the amount of contingent income transfers the principal makes to cattle suppliers, the cost of using a traceability system, and the cost to the packer of discarding beef cuts with lesions. The function [E.sup.SB](.) is the second-best expected cost per head to the principal: (1)

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

where g(.) is the function that gives the cost ($/head) of tracing an animal through a meat packing plant as a function of t [member of] T; g(.) is increasing in t such that a packer can invest in a less expensive system with lower reliability or a more expensive system with greater reliability; and the cost to the packer of discarding beef cuts ($/carcass side) with a lesion is denoted as: [p.sub.c] [greater than or equal to] 0 for a lesion in a chuck steak, [p.sub.r] [greater than or equal to] 0 for a lesion in a round steak, and [p.sub.s] [greater than or equal to] 0 for a lesion in a sirloin steak.

A Cattle Feeder's Expected Utility Function

A cattle feeder's (agent's) utility function U: [R.sup.2] [right arrow] R is specified according to the following formulation proposed by Grossman and Hart (1983, p. 10):

(2) U([I.sub.l,(j)], [a.sub.i]) = k([a.sub.i])u([I.sub.l,(j)]) - d([a.sub.i])

where U(.) is a von Neumann-Morgenstern utility function and u(.) is a Bernoulli utility function as defined by Mas-Collel, Whinston, and Green (1996, p. 184).

Using equation (2), an agent's expected utility per carcass side for a given action, and conditional on the incentive mechanism set by the principal as a 10-tuple (t, [I.sub.0*], ..., [I.sub.1,(c,r,s)]) is defined as equation (3):

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The relevance of this specification depends on whether cattle are actually marketed on a carcass side basis as defined. RTI International (2007, pp. 1-15) reports that fed cattle are primarily valued on a "per-head basis, live-weight basis or carcass weight basis or on an accumulated value of individual cuts" through the use of packer grids rather than as a multihead batch average. Therefore, the specification of the agent's utility on a per-head basis is the most appropriate. However, doing so also allows lesions to occur on both sides simultaneously resulting in an increased number of possible lesion events per carcass (the possibility of all combinations of lesions occurring on one or both sides of a carcass), but with most of them having nearly a zero probability of occurrence. Therefore, reducing the utility specification to a carcass-side basis is a further simplification that makes the model easier to solve and is nearly an exact estimate as a whole carcass-based estimate. (2)

We conduct all numerical exercises using a multiplicative separable utility function that includes all the conditions to obtain a well-behaved problem (Grossman and Hart 1983, p. 38). Therefore, we set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and d([a.sub.i]) = 0 resulting in a von Neumann-Morgenstern utility function represented as

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where k is the coefficient of constant risk aversion and [c.sub.a] is the cost of undertaking an action [a.sub.i] [member of] A.

Setting equation (2) as a constant absolute risk aversion (CARA) utility function like equation (4) allows the cost ([c.sub.a]) of a feeder action, [a.sub.i], to be expressed as negative income. The CARA specification eases the interpretation of the resulting incentive mechanisms (Haubrich 1994), and allows for modeling an increase in risk aversion by simply augmenting the value of k.

The principal-agent game with traceability is solved as a two-step numerical optimization by adapting the solution framework developed by Grossman and Hart (1983). In the first step, program (5) is solved for each combination of [a.sub.i] [member of] A and t [member of] T. The second step consists of selecting the lowest expected cost per head among those calculated in the first-step and its corresponding incentive mechanism ([I.sub.0*], ..., [I.sub.1,(c,r,s)]):

(5a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to:

(5b) U ([a.sub.i]|t, [I.sub.0*], ..., [I.sub.1,(c,r,s)]) [greater than or equal to] [bar.U]

(5c) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

where U ([a.sub.i] | t, [I.sub.0*], ..., [I.sub.1,(c,r,s)]) is set as in equation (3); [bar.U] is an agent's opportunity utility calculated as trading with a meatpacker who does not use traceability and pays the market price for a carcass side; [P.sub.l,(j)] is the probability of a particular lesion outcome given injection [a.sub.i]; and [P'.sub.l,(j)] is the probability of a particular lesion outcome from an injection [a.sub.-i] that is other than injection [a.sub.i].

Equation (5b) gives the individual rationality or participation constraint, whereas equation (5c) gives the two incentive compatibility constraints. All constraints have been set to certainty equivalents to facilitate the numerical solution of the program.

Parameter Identification

Parameters for the numerical solution include: the cost of injections at different locations, the frequency of lesions, the reservation value for cattle, the cost to the packer of discarding beef cuts with lesions, and the cost of traceability for each level of reliability (t).

The costs of injections are taken from Hilton (2005) and Griffin (2005). However, frequencies of lesions are complicated by several issues. First, an injection given in the muscle may or may not result in a lesion (Field and Taylor 2004). Second, Dexter et al. (1994) found that a majority (on average 85%) of the blemishes in top sirloin butts originated at the cow-calf, stocker, or very early in the finishing stages. No data are available for other cuts so we assume it is the same for them. From this we deduce that on average about 15% (100%-85%) of lesions clearly originate in the feedlot. If we assume that those occurring in the cow-calf, stocker, or early finishing stage are uniformly distributed, then another 28% (85%/3) are attributed to the early feedlot stage. Therefore, we assume that 43% of lesions originate in the feedlot and the remaining 57% originate at an earlier stage of production outside the control of the feedlot. Lesions can occur even when the needle-free injection is used by the feeder because cattle could have been needle injected at the cow-calf and stocker stages.

Using the assumption that 43% of lesions originate in the feedlot and the values reported by Griffin (2002), Roeber et al. (2000), and Morgan, Tittor, and Lloyd (2004) for the expected frequency of injection-site lesions in beef retail cuts, we calculated the expected frequency of an injection-site lesion for each feeder's action and the cost parameters as presented in table 1.

The reservation value for cattle is the value the feeder can obtain by delivering the cattle to a packer that does not use traceability. Assuming that an average carcass weighs 787 pounds and can be sold for $1.22 a pound in the fed cattle spot market (Roeber et al. 2000, p. 94), the feeder has a risk-free alternative of selling a carcass side at $480. Cattle feeders are averse to the risk of being identified by traceability and to account for this a coefficient of absolute risk aversion is set equal to 0.75. (3)

Discarding beef cuts with lesions is the greatest recurring cost in the simulation. Using the same procedure as Roeber et al. (2000, pp. 98-100), the opportunity costs of a lesion occurring in a top sirloin butt ([p.sub.s]), a bottom-round ([p.sub.r]), or a chuck steak ([p.sub.c]) are calculated as $11.02, $9.91, or $2.50.

Pape et al. (2003) estimate that a traceability system using radio frequency identification technology with a 38.9% traceback success rate for a small-sized (800 head per day) packing plant would cost approximately $0.11 per head. Other levels of success are not available, so we use a cost function (equation (6)) from Prendergast (1999) to represent the relation between traceability cost per head and its success rate, t.

(6) g(t) = [gamma][t.sup.2]/2

where [gamma] > 0 is a constant.

Considering that g(t = 0.389) equals 0.11, we solve equation (6) for the value of [gamma]. Using this value we calculate the costs of traceability systems, g(t), with 43.7% and 95% success rates to be $0.139 and $0.656 per head.

Using these parameter values, we obtain numerical solutions to the principal-agent with traceability game using macros built with Visual Basic for Applications linking Microsoft Excel and Microsoft Excel Solver. The nonlinear program (5) is numerically solved with the Microsoft Excel Solver that uses the Generalized Reduced Gradient (GRG2) nonlinear optimization code.

Scenarios and Results

The baseline scenario is the first-best scenario in which feeders and packers have symmetric information. The second scenario represents the current situation of injection-site lesions with no traceability The third scenario evaluates traceability as a second-best solution when information is asymmetric and the traceability system's reliability varies.

Symmetric Information Scenario

Under symmetric information, any action undertaken by a cattle feeder (agent) is freely observable by the packer, which eliminates the reason for using traceability. The packer, considering the expected costs of lesions and payments, first chooses the certain amount of money, [I.sub.FB] to be transferred to feeders for each action ([a.sub.i]), and then contracts the action that leads to the lowest expected cost. Thus, in the first-step program (7) is solved to find [I.sub.FB] for each [a.sub.i] [member of] A. In the second step the action that leads to the lowest expected cost is then chosen:

(7a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to:

(7b) k([a.sub.i])u([I.sub.FB])-d([a.sub.i]) [greater than or equal to] [bar.U]

where the function [E.sup.FB.sub.c] (.) is the first-best expected cost per head to the packer, [P.sub.0] is the probability of no lesion, [P.sub.c] is the probability of a lesion in the chuck, and so on.

The symmetric information scenario's probabilities are calculated as [P.sub.0] = (1 - [F.sub.c]([a.sub.i]))(1 - [F.sub.r]([a.sub.i])) (1 - [F.sub.s]([a.sub.i])), [P.sub.c] = [F.sub.c]([a.sub.i])(1 - [F.sub.r]([a.sub.i]))(1 - [F.sub.s]([a.sub.i])), [P.sub.r] = (1 - [F.sub.c]([a.sub.i]))[F.sub.r]([a.sub.i])(1 - [F.sub.s]([a.sub.i])), and so on. There are eight contingencies because the identity of an agent is always known (t = 1) without any cost. Each contingency's probability is presented in table 2.

Participation constraint (7b) always binds at the optimum because [E.sup.FB.sub.c](.) and u(.) are strictly increasing in the first-best income transfer, [I.sub.FB]. The packer offers a transfer for each action, that is just enough to fulfill an agent's reservation utility. The optimal level of utility for an agent is found by solving equation (8):

(8) u([I.sup.*.sub.FB]) = ([bar.U] + d([a.sub.i]))/k([a.sub.i]).

Finally, the first-best income transfer conditioned on action [a.sub.i] is calculated as

(9) [I.sup.*.sub.FB] = [upsilon](u([I.sup.*.sub.FB]))

where [upsilon](.) denotes the inverse of the Bernoulli utility function u(.).

The complete cost of lesions to the packer and the income transfers made by the packer to the feeder under various injection actions are shown in table 2. This shows that the lowest expected cost to the packer ([E.sup.FB*.sub.c] = $962.50 per head) occurs when a feeder gives all injections with a needle-free technique. The meat packer would contract the feeder to give all injections with a needle-free technique by offering a constant income transfer of $480.20 per carcass side. The value of a carcass side in the market is $480, so $0.20 per carcass side is the price-premium the packer pays the feeder to cover the additional costs a feeder incurs to give needle-free injections. The feeder will comply with the contract because the packer can observe the action and punish the feeder if the contracted action is not the one observed.

Second-Best Scenarios--Injection-Site Lesions Without Traceability

The current situation in the beef industry is broadly characterized as one of information asymmetry and no traceability so that the packer cannot create incentive mechanisms based on observed lesions. The equilibrium for this scenario is for the packer to pay the market price of $960/head, and for a feeder to give all injections in the rear leg because this is a zero-cost action. The expected costs for the second-best scenario without traceability must equal the expected costs for the symmetric information scenario because the feeder has no motivation to incur the costs of moving injections from the leg. Therefore, the expected cost for a meat packer is $963.29 per head as presented in table 2.

Second-Best Scenarios--Injection-Site Lesions with Traceability

With asymmetric information and with traceability the two-step optimization procedure discussed in the context of program (5) is used. However, it is first necessary to ensure that the Monotone Likelihood Ratio Conditions (MLRCs) are satisfied (Salanie 1997, p. 118) by checking if the probability conditions (10) hold for all contingencies m preferred to -m by the packer:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where action [a.sub.i] is more costly to agents than action [a.sub.j].

We found that the probabilities in our model do not fulfill the MLRCs. Therefore, we impose eight additional constraints (11) on program (5) to ensure that the contingent income transfer ([I.sub.l,(j)]) will be higher as the outcome is more preferred: (4)

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Results obtained by solving the first step of the principal-agent game with traceability are presented in tables 3 and 4. The minimum expected costs presented in the third column of table 3 are calculated by evaluating the income transfer mechanism for each combination of a cattle feeder's injection action and the traceability success rate.

Using the results in table 3, we choose the combination of the cattle feeder's injection action and traceability success rate that leads to the lowest expected cost to the packer. The lowest expected cost is $962.82 per head (table 3) and is achieved if agents are induced to give all injections with a needle-free technique (action 3) using a traceability system with a 38.9% success rate. The incentive mechanism that induces the feeder to give all injections with a needle-free technique (action 3) is a traceability system that works with 38.9% accuracy and with income transfers as given in table 4.

These results show that $480.32 per carcass side, [I.sub.0*], is transferred if the traceability system fails to work. If the traceability system works then $480.35 per carcass side, [I.sub.1,0], is transferred when no damage is observed, $480.32 per carcass side, [I.sub.1,c], is transferred if at least one injection-site lesion is observed in chuck steak, and so on as presented in table 4. When traceability works, all contingencies (except for a lesion in a chuck steak) imply a punishment of the feeder because the income transfers are less than $480 (the market value of a carcass side). Feeders are rewarded with income transfers greater than $480 per carcass side for contingencies in which traceability fails to work, traceability works properly and no damage is observed, or only damage in the chuck is observed.

The probability of income transfers are shown in table 4. For the low level of trace-back and the needle-free injection method, the transfer [I.sub.0*]. = $480.32 per carcass side occurs 61.1% of the time, [I.sub.1,0] = $480.35 per carcass side occurs 32.30% of the time, and so on. Using these values, the expected transfer to feeders is $480.33 per carcass side, which means the packer pays an average price-premium of $0.33 per carcass side to get feeders to accept this incentive mechanism. This price-premium pays the higher costs the feeder incurs to give all injections with a needle-free technique ($0.204/carcass side) plus a risk-premium ($0.126/carcass side).

The income transfers appear to vary little across contingencies, but only in comparison to the price of a carcass side. To place the income transfer in perspective, the packer pays roughly a 62 % incentive payment over the cost of injections to entice the feeder to use needle-free injections, so the incentive payment from this perspective is high. The low values also mask the variability of transfers compared with the expected losses the principal incurs when a lesion is observed. For instance, the loss to the principal of a lesion in the chuck, in the round, and in the sirloin is $23.43 per carcass side ($2.50 + $9.91 + $11.02) but occurs only in 0.004% of the cases making the expected loss ($0.00094) practically zero.

Comparing Scenarios

The first-best or symmetric information scenario solution is compared with the second-best solution by calculating min{[E.sup.WT*.sub.c], [E.sup.SB*.sub.c]} - [E.sup.FB*.sub.c], where [E.sup.WT*.sub.c] and [E.sup.SB*.sub.c] are the minimum expected cost per head for the second-best scenarios without and with traceability, and [E.sup.FB*.sub.c] is the minimum expected cost per head for the symmetric information (first-best) scenario. The result of this calculation is: min{963.29, 962.82} - 962.50 = $0.32 per head. This figure gives the cost of asymmetric information and agency costs, defined as the cost due to the separation of ownership and management. The agency cost is mitigated by the use of incentive mechanisms and eliminated by vertical integration of the packer and feedlot.

The value of traceability is given by [E.sup.WT*.sub.c] - [E.sup.SB*.sub.c], which is $963.29 - $962.82 = $0.47 per head. An 800 head per day plant, as assumed in the studies supplying the parameters, would save approximately 800 head x $0.47 per head = $376 per day. Extrapolating this to the entire steer and heifer slaughter of 27.3 million head in 2006 would result in a savings of approximately $12.8 million per year for the beef industry. Therefore, the reduction in the losses from injection-site lesions by inducing cattle feeders to give needle-free injections offsets the costs of a traceability system and the payment of price premiums to compensate agents for accepting a risky payment scheme and using the more costly needle-free injection.

Sensitivity Analysis

The case of injection-site lesions is representative of a broad class of problems in the food chain where an upstream agent's actions affect downstream product attributes that cannot be source verified when the problem is discovered. To further generalize the results, a sensitivity analysis of the key variables affecting the value of traceability is conducted.

The primary factors affecting the economic value of traceability include the level of risk aversion of the agents, the agents' ability to affect the outcome of a product attribute, the cost of the traceability system to the principal, and the cost of agents' actions. To consider how these factors interact, we simulate the model with nine values for the absolute risk-aversion parameter k [member of] (0.125, 0.250, ..., 1.125), nine different values for the percentage of lesions that originate in the feedlot (PLOF) [member of] (0.33, 0.40, 0.43, 0.50, 0.60, ..., 0.90, 0.95) and nine different values for the costs of the traceability system as percentage mark-ups over the base cost estimates x [member of] (1, 1.5, ..., 5). For instance, by multiplying the base traceability costs by 1.5 we simulate a 50% increase in costs. Finally, we simulate the models using nine different values for the cost of agents' actions by multiplying the base values of each injection action by a factor y [member of] (1, 1.1, ..., 1.8). For instance, by multiplying the base value of an injection action by 1.1 we simulate a 10% increase in its cost. To isolate the impact of each variable, and reduce the computational complexity, we ran simulations for each of the nine values of a given variable holding all other variables equal to their baseline values in the previous results. This reduced the combinations of sensitivity results from 6,561 to only 33 combinations (the baseline is a common scenario among all variables).

For each simulation we calculate the value of traceability according to [E.sup.WT*.sub.c]--[E.sup.SB*.sub.c] so that we generated a series of 33 values for the value of traceability. Using the values obtained with the simulations we estimated the following sensitivity model using ordinary least squares (OLS) regression:

Value of Traceability

= - 0.2613--0.0198x--0.6658y

- 0.0362 ln(k) + 3.2622(PLOF),

[R.sup.2] = 0.9976.

The estimated model shows that a 10% increase in the base traceability cost would cause a reduction of $0.00198 per head in the value of using a traceability system. If the base cost of traceability increased more than five times, traceability would not have economic value.

For an increase of 10% in the base agents' cost of actions the value of traceability decreases by $0.06658 per head. At an increase of 70%, the value of traceability becomes zero because the expected loss with injection lesions becomes less than the cost of the incentive required for the feeder to give either a needlefree injection or an injection in the neck area.

The value of a traceability system decreases (0.0362[k.sup.-1]) with the coefficient of absolute risk aversion (k) of agents at increasing rates (0.0362[k.sup.-2]). In the limit, a very high k implies the need for paying such high risk-premiums to agents that a traceability system might become economically infeasible. For each 10% increase in the effect of cattle feeder's action on the final frequency of a lesion (PLOF) the value of traceability goes up by $0.3262 per head. This result shows that the less the upstream party (feedlot) can do to mitigate a problem, the lower the value of traceability will be.

For all simulations the traceability system with a 38.9% success rate of linking the cut to the cattle feeder is the one optimally chosen by the packer. This illustrates that the results are robust with regard to the underlying factors affecting investment decisions in traceability, and that even a relatively imperfect system can be sufficient to enforce first-best behavior in agents.

Conclusions

One of the key implications of traceability is that it has the potential to reduce information asymmetry in the supply chain, resulting in improved allocation of economic value. The case of injection-site lesions in beef is used to numerically simulate the economic value that can be attained through a reduction in information asymmetry. To accomplish this, the general two-step procedure developed by Grossman and Hart (1983) is used to model and solve a principal-agent model wherein a meat traceability system is in place to affect the decision of injection-site choice in cattle.

Simulation results based on technical data on injection-site lesion incidence show that by allowing the packer to create and use incentive mechanisms, a meat traceability system could induce feeders to adopt the quality-control practice preferred by the meat packer. The income transfers resulting from the incentive mechanism are small in absolute terms, but relatively large compared to the costs of alternative injection methods defined by the case study.

The optimal traceability success rate is also examined, with a higher success rate achieved through greater investment costs. We found that the lowest traceback success rate (38.9%) is the optimal rate chosen by the packer. This finding has important policy implications, because one of the major concerns of implementing traceability is its expense and reliability.

This result shows that even a relatively unreliable system acts as a credible deterrent and induces actions that meet the objective of improved quality and economic value allocation.

The main analytical contribution of this work is to provide a numerical framework for the principal-agent problem representative of a class of problems characterized by an attribute negatively affecting the value of a product that can only be discovered after the sale is made and the supplier can no longer be identified. Other works have focused on cases where testing or grading could be completed at the time of the transaction so that the supplier could be penalized or rewarded immediately.

Although we address the relatively minor issue of injection-site lesions, it is readily applicable to other more pressing issues. These include issues such as feeding animal by-products to cattle, which can lead to mad cow disease, or the misuse of feed additives, which can leave residue in meats. The latter issue is becoming increasingly important in meat export markets and has implications beyond domestic meat production.

[Received October 2006; accepted January 2008.]

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(1) We assume the two carcass sides of an animal are independent from each other, so that the final expected cost per head is twice as much as the cost of each carcass side.

(2) Although carcasses are individually valued by the packer, the cattle feeder may view the payments as an average for a batch of cattle, say a delivered truckload. In this case the variance of contingencies on a carcass basis assumed by the model would overstate the individual carcass incentive payments necessary to compensate a risk-averse batch averaging cattle feeder. Therefore. if we modeled payments on a batch basis we would find lower contingency payments would be necessary for the same variability across contingent outcomes. Assuming the mechanisms created in the "batch" model still satisfy the incentive compatibility constraints, the costs (payments to cattle feeders) for the principal (packer) would be reduced and the second-best value of the traceability system would increase. We maintain the individual carcass pricing scheme because the batch combinations of lesions along with combinations of traceability system success rates dramatically increase the computational difficulty without substantially improving the characterization of the problem.

(3) Hardaker et al. (2004, p. 109) classifies farmers who are somewhat risk averse or normal as having a coefficient of relative risk aversion equal to 1. The proportional net worth of a cattle feeder to equilibrate relative and absolute risk aversion can be found by dividing 1 by 0.75 to obtain a value of 1.33. Using the same measurement scale as employed by Haubrich (1994, p. 264), a feedlot should then have a net worth of $1.33 million. This is the same as marketing 1,386 animals at an average price of $960 per head. RTI International (2007) reports that cattle-feeding operations with 500 or more head account for 42% of cattle inventories and half of those cattle are on operations with 1,000 or more head. Therefore, it is reasonable to set the coefficient of absolute aversion equal to 0.75.

(4) When no lesions are found and the traceability system works properly, the expected economic loss will be the lowest among all possibilities and the constraints are consistent with this. The second lowest expected loss occurs when the traceability system fails because it is possible that no lesion has been found that yields a lower average loss compared with other contingencies. The other constraints follow the same idea; a lesion in the chuck causes a lower economic loss than if it is in the bottom-round, and a lesion in the bottom-round causes lower loss than a lesion in the top sirloin.

Moises A. Resende Filho is assistant professor, Departamento de Analise Economica, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil, and Brian L. Buhr is professor and E. Fred Koller Chair in the Department of Applied Economics, University of Minnesota.

The authors thank Professor Walter N. Thurman for editorial assistance, Professor Robert P. King for earlier assistance with the model solution, and two anonymous reviewers for their very helpful comments. Partial funding support was provided by the Center for Agricultural and Rural Development (CARD) at Iowa State University, Ames, IA. All remaining errors are the authors'.

Table 1. Value of the Parameters of the
Principal-Agent Model

                                      Expected
                                    Frequency of
                                   Injection-Site
                                   Lesion in Top
                     Costs of      Sirloin Butt,
                      Action         [F.sub.s]
Agent's           ($ Per Carcass    ([a.sub.i])
Action                Side)             (%)

Give all          Base cost = 0         2.50
  injections in
  the rear leg

Give all           $0.17 more           1.43
  injections in   than rear leg
  the neck area

Give all           $0.204 more          1.43
  needle-free     than rear leg
  injections
                                      Expected
                                     Frequency
                                         of
                     Expected        Injection-
                   Frequency of         Site
                  Injection-Site     Lesion in
                    Lesion in       Chuck Steak,
                  Bottom-Round,      [F.sub.c]
                  [F.sub.r],         (a.sub.i)
Agent's            ([a.sub.i])         F,(ai)
Action                 (%)              (%)

Give all              11.30             9.98
  injections in
  the rear leg

Give all               6.44            17.50
  injections in
  the neck area

Give all               6.44             9.98
  needle-free
  injections

Source: Costs of actions were estimated based on Hilton (2005)
and Griffin (2005). Frequencies are calculated based on Roeber
et al. (2000), Griffin (2002), and Morgan, Tittor, and
Lloyd (2004).

Table 2. Expected Cost to the Principal, Income
Transfers to Agents, and Probability of Injection-Site
Lesions Based on Agent's Injection Method Under Symmetric
Information

                         Probability of Injection--
                         Site Lesion Occurrence (%)

Agent's
Injection      [P.sub.O]    [P.sub.c]   Pr P(c.r)   [P.sub.r]

In leg          77.856        8.627       9.919       1.996
In neck         76.086       16.140       5.238       1.100
Needle free     83.026        9.200       5.716       1.200

                      Probability of Injection--
                     Site Lesion Occurrence (%)

Agent's
Injection       P(c,s)       P(r,s)     P(c,r,s)

In leg           0.221        0.254       0.028
In neck          0.233        0.076       0.016
Needle free      0.133        0.083       0.009

               Expected                  Income
                 Cost                   Transfers,
                to the                     IFB
              Principal,                ($/Carcass
Agent's          E CB                     Side)
Injection      ($/head)                  In leg

                963.29                   480.00

In neck         962.81                   480.17

Needle free    962.50 *                  480.20

Note: For [P.sub.j], j = 0 for no lesion, j = c for lesion
in chuck, j = r for lesion in bottom round, j = s for lesion
in sirloin. Combinations indicate multiple lesions. An
asterisk (*) denotes the overall minimum expected cost
to the principal.

Table 3. First-Step Results to the
Principal-Agent Game with Traceability

          Traceability
            System's      Expected
            Expected        Cost,
            Traceback      [E.sup.
Agent's      Rate of      SB.sub.c]
Action     Success (%)    ($/head)

  (1)         38.9         963.40
  (2)         38.9         963.08
  (3)         38.9         962.82 (*)
  (1)         43.7         963.43
  (2)         43.7         963.11
  (3)         43.7         962.84
  (1)         95.0         963.95
  (2)         95.0         963.62
  (3)         95.0         963.35

Note: (1) denotes the action of giving
all injections in the rear leg,
(2) refers to the action of giving all
injections in the neck area, and
(3) stands for the action of giving all
injections with a needle-free technique.
An asterisk (*) denotes the overall
minimum expected cost to the principal.

Table 4. Incentive Mechanisms from the First-Step Solution
to the Principal-Agent Model with Traceability and
Expected Frequencies of Occurrence of Each Contingency

          Traceability
            System's
            Expected
           Traceback
            Rate of                    Income Transfers
Agent's     Success
Action        (%)        [I.sub.0 *]   [I.sub.1,0]    [I.sub.1,c]

($/Carcass Side)

(1)           38.9         480.00         480.00        480.00
(2)           38.9         480.27         480.27        480.27
(3)           38.9         480.32         480.35        480.32
(1)           43.7         480.00         480.00        480.00
(2)           43.7         480.28         480.28        480.28
(3)           43.7         480.32         480.35        480.32
(1)           95.0         480.00         480.00        480.00
(2)           95.0         480.30         480.30        480.30
(3)           95.0         480.32         480.36        480.32

                           Probability of each Contingency Occurring

                         [P.sub.0] *   [P.sub.1,0]    [P.sub.l,c]

(1)           38.9          61.10         30.29          3.36
(2)           38.9          61.10         29.60          6.28
(3)           38.9          61.10         32.30          3.58
(1)           43.7          56.30         34.02          3.77
(2)           43.7          56.30         33.25          7.05
(3)           43.7          56.30         36.28          4.02
(1)           95.0          5.00          73.96          8.20
(2)           95.0          5.00          72.28          15.33
(3)           95.0          5.00          78.87          8.74

                      Income Transfers

Agent's                   [I.sub.1,
Action    [I.sub.1,r]      (c,r)]      [I.sub.1,s)]

                      ($/Carcass Side)

(1)             480.00     480.00         480.00
(2)             479.70     479.70         479.70
(3)             479.75     479.75         479.75
(1)             480.00     480.00         480.00
(2)             479.69     479.69         479.69
(3)             479.75     479.75         479.75
(1)             480.00     480.00         480.00
(2)             479.69     479.69         479.69
(3)             479.77     479.59         479.77

            Probability of each Contingency Occurring

                          [P.sub.l,
          [P.sub.l,r]      (c,r)]      [P.sub.1,s)]

                             (%)

(1)               3.86      0.43           0.78
(2)               2.04      0.43           0.43
(3)               2.22      0.25           0.47
(1)               4.33      0.48           0.87
(2)               2.29      0.49           0.48
(3)               2.50      0.28           0.52
(1)               9.42      1.04           1.90
(2)               4.98      1.06           1.04
(3)               5.43      0.60           1.14

Agent's    [I.sub.1,      [I.sub.1,     [I.sub.1,
Action       (c,s)]        (r,s)]        (c,r,s)]

($/Carcass Side)

(1)             480.00     480.00         480.00
(2)             479.70     473.33         473.33
(3)             479.75     473.87         470.93
(1)             480.00     480.00         480.00
(2)             479.69     473.49         473.49
(3)             479.75     474.04         471.09
(1)             480.00     480.00         480.00
(2)             479.69     474.69         474.69
(3)             479.59     475.23         472.23

Probability of each Contingency Occurring

           [P.sub.1,      [P.sub.1,     [P.sub.1,
             (c,s)]        (r,s)]        (c,r,s)]

(1)               0.09      0.10          0.011
(2)               0.09      0.03          0.006
(3)               0.05      0.03          0.004
(1)               0.10      0.11          0.012
(2)               0.10      0.03          0.007
(3)               0.06      0.04          0.0004
(1)               0.21      0.24          0.027
(2)               0.22      0.07          0.015
(3)               0.13      0.08          0.009

Note: (1) denotes the action of giving all injections in
the rear leg, (2) refers to the action of giving all
injections in the neck area, and (3) stands for the action
of giving all injections with a needle-free technique.