Empirical Calibration of a Least-Cost Conservation Reserve Program

compound error term (v0 - ln θ) is positively skewed with third central moment equal to
—σ³ (1 — 4∣π) p2∣π.

Let e ≡ (e1, ..., eS)⁰ denote the residuals for Eq. (8) of a regression of the system
comprising Eqs. (6)-(8). The third moment of the residuals is a consistent estimator for the
third moment of the combined error term. This suggests an additional equation that can be
estimated sequentially after Eqs. (6)-(8):

e3 = —σ³ (1 — 4∣π) p2∣π + Vn+ɪ,                         (9)

where Vn+ɪ is random noise. The estimate σ³ can then be used to correct the initial bias in
β₀. Adapting Newey (1984), one can employ the residuals from Eqs. (6)-(8) to compute the
asymptotic covariance matrix for the entire system.

Using these results, estimation of the system proceeds in three steps. In the first
step, I ignore ln θ, and estimate Eqs. (6)-(8) by system two-stage least squares (2SLS). This
procedure generates consistent estimates of all parameters, except β₀ . Although otherwise
consistent, the 2SLS estimator is likely to be inefficient and generate inconsistent estimates
of the covariance matrix. In addition to correlation of errors for the same observation across
equations, the noise component may be heteroskedastic or influenced by unobserved shocks
commonly affecting all producers in the same geographic area. Such shocks may be short-
lived or persist across time.

I account for these potential problems in the next step. Following Pepper (2002),
Wooldridge (2002), and Wooldridge (2003), the 2SLS residuals are used to construct a more
robust GMM estimator. This estimator is asymptotically efficient in the presence of ar-
bitrary heteroskedasticity and arbitrary county-level correlations both within and between
time periods. Finally, the third moment of the GMM residuals from Eq. (8) provide the

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