The name is absent

Table 4. Summary of Average Revenue and Efficiency Measures by Acreage and Gross Revenue Class for
Six-year Average Period for 170 Central Illinois Grain Farms

'SeeTabIe 2 for definitions of R, POTR and CRTSR.

inefficiency decreases and scale inefficiency in-
creases. This pattern is similar to the change in the
decomposition of inefficiency noted by Moll. To
provide further insight into this change, the optimal
farm size and returns to scale measures are examined
using the 6-year average data. Sets of the efficiency
estimates are generated, one for each of three data
sets: “total,” “small,” and “large.” The “total” data
set represents the entire 170 farms for the six-year
average data. The “small” and “large” samples in-
clude only the 85 smallest and largest farms, respec-
tively, in the “total” data set.

A ray-homothetic function is estimated for each of
the samples. Based upon the estimated coefficients,
the optimal output (OPTR), the returns to scale
measure (u),¹² the levels of inefficiency, and the
efficiency ratios are calculated (Table 5). Within
each data set (total, small and large), the average
values of these variables are also reported for the
smallest and largest farms.

Several points emerge from Table 5. First, the total
efficiency measures for both the small and large data
Sets are higher than for the total data set. Grouping
the farms into similar size classes increases sample
efficiency measurement. Second, regardless of the
sample, decreasing returns to scale are evidenced.
The average returns to scale measure, u, is always
less than 1 for each of the complete samples (total,
u = 0.76; small, u = 0.64; large, u = 0.81). Also,
within each data set, the large farms exhibit greater
pure technical efficiency and larger scale inefficien-
cies than do the small farms. Furthermore, for all the
data sets, u is greater than one (increasing returns)
for some small farms and less than one for larger
farms.

The scale inefficiency increases with farm size
because of the form of the ray-homothetic function
and because the optimal level of output (OPTR) does
not change substantially within any of the data sets.
For example, for the total data set, OPTR averaged
$201,951 with a standard deviation of only $1,163.
However, the actual revenue (R) of these farms
ranged between $48,556 and $403,450. Further in-
spection of the factor shares for small and large
farms revealed limited variability across size as the
reason for a relatively constant OPTR.

It also appears that the ray-homothetic function
classifies farms as being either scale efficient or
scale inefficient depending upon the sample. For
example, the smallest 85 farms in the total data set
are found to be operating at approximately constant
returns to scale (u=1.01). However, when only these
farms are used (the small data set) in the estimation,
substantial scale inefficiencies are identified
(u=0.64: farms are operating at decreasing returns).
This identifies the importance of the appropriate
definition of the representative sample.

The findings here provide some insight into the
Moll and Grabowski dialogue regarding the RHF.
First, for the three samples (total, small, and large)
the specification of the RHF appears to impose
increasing returns to scale on the smallest farms and

¹²The returns to scale measure, or function coefficient, for this specification of the ray-homothetic function is:
u = (<XfKt + o⅛K_p + α_sK_s + a_cK_c + o⅛Kb ⁺ a_nK_n + a∣Kι / R.

If u= 1, constant returns to scale are exhibited. Increasing returns are indicated by u> 1 and decreasing returns by u< 1.

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