The name is absent

R = lnα_o + α_fK_flnF + a_pK_plnP

.    + a_sK_slnS + a_cK_clnC

+ a_bK_blnB + a_nK_nlnN

+ aιKιlnL

was estimated, where R denotes gross (accrual) farm
revenue and F, P, S, C, B, N, and Lrepresent accrual
fertilizer, pesticides, seed, capital (power and equip-
ment), buildings, labor, and land expenditures, re-
spectively. All measures of receipts and
expenditures are on a total farm basis.⁵ Capital in-
cludes expenditures on utilities, machinery repair
and hire, fuel, oil, and machinery depreciation.
Building expenditures include drying, storage, and
building repair and depreciation. Labor includes
both hired labor and operator’s unpaid labor.⁶ The
land expenditure was calculated by multiplying an
interest charge⁷ times a total land value and reflects
the net rents which a landlord would receive each
year. The land value was market-based and deter-
mined by FBFM according to an index which values
different parts of the farm according to soil-specific
SPRs. Table 1 presents average values of these
variables, acreages, and yields over the six-year
period (averages of six-year average faπn values).
The K_i (i= f,p,s,c,b,n,l) are expenditure shares and
the α_i are the parameters to be estimated. Equation
(1) was estimated using ordinary least squares.⁸

To determine the extent to which farms are effi-
cient in a technical sense, a corrected ordinary least
squares (COLS) method was used. The potential
output of the sample of farms was calculated by
adjusting the intercept of (1) upward by the largest
residual. This procedure ensures that production
falls within the efficient frontier. The level of pure
technical inefficiency for each farm was then calcu-
lated by subtracting actual revenue from potential
revenue, which was generated by using actual farm
values of the inputs and expenditure shares in the
adjusted equation (I).

The extent to which farms are efficient in a scale
sense was also examined. The procedure described
in Aly et al. was used to identify the extent of scale
inefficiency by farm. From equation (1), the level of
output under constant returns to scale is expressed
as a function of the expenditure shares:

OPTR = α_fK_f + a_pK_p + a_sK_s + a_cK_c

+ a_bK_b + a_nK_n + a₁K_l.

This optimal level of output (OPTR) was adjusted
upward or downward along a constant returns to
scale function according to each particular farm’s
level of input use to calculate a farm’s constant
returns to scale revenue. The level of scale ineffi-
ciency was then derived by subtracting potential

⁵The data were not deflated over the six-year period. While deflating would change the levels of actual and estimated revenues,
it would not affect the efficiency ratio estimates or other inter-year comparisons discussed in this analysis.

⁶The total unpaid labor is the product of a monthly labor rate and the number of months of unpaid labor. The monthly
operators’ unpaid labor rate is defined uniformly over all farms within each year. The monthly unpaid labor rates ($/month) are;
1982:1075, 1983-1984: 1100,1985-1986:1150,1987:1225. The total expenditures on unpaid labor differ for each farm as the
number of months of unpaid labor varies.

⁷The interest charge calculated by FBFM is based upon observed rental returns from farms with crop-share leases. These rates
are: 1982: 2.8 percent, 1983-1984: 3.2 percent, 1985: 4.2 percent and 1986-1987: 5.0 percent.

⁸The original data set included 197 farm observations, In practice, all frontier estimations (whether deterministic or stochastic)
are sensitive to outliers, and no definitive methodology exists for identification purposes. Because of this, a method that examines
the regression residuals of the six yearly estimations was used. Observations whose regression residuals were greater than plus or
minus two standard deviations in any one of the six years were eliminated from the analysis. This resulted, in any particular year, in
from four to seven percent of the farms being eliminated from the sample. While the elimination of what may appear to be some of
the most technically efficient and inefficient farms from the sample may appear undesirable, in reality some allowance must be
made in frontier estimation for data outliers. In addition, the resulting sample (which includes 170 farms) still exhibits a rather wide
range of total and pure technical efficiency estimates.

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