Empirical Calibration of a Least-Cost Conservation Reserve Program

sup_q {pq — C (w, q, a, θ)}. Let q* be the profit-maximizing output quantity. Algebraic ma-
nipulation of the first order condition for an interior solution to the profit maximization
problem yields the following expression of ratio of revenue to cost:

pq*        ∂ ln C (w, q, a, 1)

C (w, q,a,θ)         ∂ ln q

Like expenditure shares (2), the ratio (3) is independent of θ.

Following Diewert (1982), Eqs. (1), (2), and (3) provide the basis for estimating
a parametric technology for profit-maximizing producers. For the cost function, I use a
modified Cobb-Douglas specification that allows the marginal return to land to vary with
farm size:

C (w,q,a,θ)=θ^-1 exp (β₀) q^{βq Q}_n w_n^βn a^{βa+βaa ln a}.                  (4)

For this specification, with cross-sectional data the system of estimating equations for a
typical observation is:

N-1                                           ₂

β0 + P β_n ln w^jn + β_q ln q* + βa ln a + β_aa (ln a)² + v0 — ln θ (5)
n=1

β_n + vn , n=1, ..., N — 1(6)

β_q + v_N ,                                                        (7)
where we ≡ (vj₁, ...,wN)0 ≡ (w₁∕wN, ...,wN/wN)0 is the vector of input prices normalized by
wN and C (we, q*, a, θ) = C (w, q*, a, θ) /wN by the linear homogeneity of the cost function
in input prices. The vector of stochastic noise for producer s is v_s≡ (v₀, v₁, ..., v_N)⁰.

Since output is endogenous under the assumption of profit maximization, in estima-
tion output price p acts as an instrument for q*. Let z_s ≡ (lna, ln a², lnwe0, lnp)0 denote the

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