Meat Slaughter and Processing Plants’ Traceability Levels Evidence From Iowa

K

(1)          T^*=β0+∑Xiβi+ε

i=1

where T^* is the unobservable dependent variable (traceability level), β₀ is the intercept
parameter, X_i for i= 1,..., K are explanatory variables, β_i for i= 1,...,Kare the
corresponding parameters, and ε is the disturbance term to the equation. The equation
(1) can be seen as a reduced form of a structure which describes the traceability decision
process of a profit maximizing firm. Souza-Monteiro and Caswell (2006)’s modeling is
in line with this approach. Souza-Monteiro and Caswell (2005) consider such a decision
problem within a principal agent framework where the customer is principal and the plant
is agent. Other structures may include hedonic pricing approach within competitive
market equilibrium. This route is taken for the food safety variable in Antle (2000). We
concentrate our efforts on the specification of equation (1) without adhering to a
particular structure.

Based on the responses to the questions which characterizes the plants’ traceability
activities (both backward and forward) in terms of breadth, depth, and the precision
dimensions in the survey, we will construct an indirect measure for traceability T as levels
1 for low, 2 for medium, and 3 for high. Then,

*
-∞≤T<μ₁,

*
μ₁≤T <μ₂,
μ₂ ≤T ^* <∞,

where the boundsμ₁and μ₂ are parameters to be estimated. Plugging T^* from (1) into (2)
and denoting the explanatory variables (intercept term included) and corresponding
parameters in matrix form as X and β, respectively yields the following in terms of
probabilities

P(T=1|X) =Λ(μ1- Xβ)

(3)                 P(T = 21X) = Λμ - Xβ) - Λ(μ - Xβ),

P(T = 3|X) =1 -Λ(μ2 -Xβ),

e^z

where Λ =-----is the cumulative probability function for logistic distribution with a

1+e^z

generic variable z .

Table 2 provides a list of possible variables that can be constructed using survey
responses. Based on the estimated parameters of these explanatory variables, the
following hypotheses will be tested.

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