Empirical Calibration of a Least-Cost Conservation Reserve Program

vector of exogenous variables for producer s.

Due to the information asymmetry, θ is inherently unobservable to the government
and the econometrician. Following the stochastic frontier approach, I treat ln θ as a random
variable. Assume that v and θ satisfy the following moment conditions:

M1. E [vs|z_s] = 0;

M2. E [v₀³] = 0;

M3. E [ln θ∣zs] = -σp2∕π;

M4. E ^£(lnθ - E [ln θ])³] = σ³ (1 - 4∕π) p2∕π.

Under M1, the vector v_s has a mean-zero disturbance vector uncorrelated with
the instruments. In addition, M2 states that the disturbance for Eq. (5) is symmetrically
distributed. Assumptions M3 and M4 require that ln θ be uncorrelated with the instruments,
and that its mean and skewness correspond to those of - ∣y∣, where y is a random variable
distributed N (0, σ²).

As noted by Aigner et al. (1977), these distributional assumptions have two practical
implications. First, consider a least squares estimator that ignores the type-dependent com-
ponent of the error structure, mistakenly using the moment conditions E [v₀ - ln θ∣z_s] = 0.
By treating the expected compound error as mean zero, rather than mean σ∖∕ⁱ2∕π, this
regression effectively replaces Eq. (5) with

N         i----∖   N^-1      w

ln C (we,q*,α,θ) = (β₀ + σ∙∖∕2∕π) + P β_i ln — + β_q ln q* + β_a ln a
n=1     wN

+βaa (ln a)² + (υ₀ - ln θ - σ p 2 n´ .                    (8)

Such an estimator generates consistent estimates of all parameters in the cost function except
βo, which is upwardly biased by σ∙ξ∕2∕π. The second practical implication is that the

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