Empirical Calibration of a Least-Cost Conservation Reserve Program

Table 2 reports the estimation results.

With these parameter estimates, profit-maximizing output can be calculated as:

2000        N

(θp)^-1 β_qexp   ^P δidi  ^Q w_n^βna^{βa+βaa ln a}

i=1997       n=1

with the corresponding profit function

For the parameter estimates in Table 2, marginal returns to land are increasing until
about 400 acres, after which the profit function is strictly concave in land cultivated. The
marginal profit from land is positive for all farms less than 6,350 acres. The marginal effect
of type on profit is positive, and the single-crossing condition π_aθ > 0 is satisfied for all farms
for which the marginal return to land is positive. In addition, this profit function satisfies
theoretical monotonicity and curvature conditions with respect to prices.

Although model specifications and data sets differ, input own-price elasticities are
comparable to results from earlier studies of U.S. agriculture such as Ray (1982). The
expected farm size for any randomly chosen acre of land in the sample is approximately
2,000 acres. The estimated average annual return to land for the typical 2,000 acre farm over
the four years is approximately $33 per acre. When combined with lump-sum government
payments of about $54 per enrolled acre, this figure is reasonably close to average farmland
rental rates for the region of $91.⁶

As we shall see in the next section, empirical characterization of the optimal con-
tract schedule requires two components: a profit function for each type of producer and a
probability distribution for type. The procedures described in this section provide precisely

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