efficiency measures over time. Additionally, often
in agriculture, part of the input expenditures (par-
ticularly for fertilizer and capital) in one year may
be carried over and applied to production in sub-
sequent years. Even if accrual revenue and expendi-
ture data are used, measurement errors may
inappropriately attribute cash expenditures for in-
puts to particular years. Furthermore, certain crop
rotation plans are known to provide beneficial yield,
weed control, and tillage effects from year to year.
Studies which examine efficiency using a single
year’s expenditure and revenue data as proxies for
inputs and outputs may not be able accurately to
account for these issues.
The ray-homothetic function (RHF) has been
widely applied in evaluating efficiency using cross-
section data (i.e., Aly et al.; El-Osta, Pelly, and
Whittaker; Elyasiani and Mehdian; Fare, Jansson
and Lovell; Grabowski and Belbase). Its use here is
primarily motivated by the differences in findings
and implications generated by its application to Illi-
nois grain farms and by a desire to examine its
usefulness in this environment (Moll).
The RHF is appealing because of its flexibility in
measuring the pure technical and scale efficiency of
individual firms and because it allows returns to
scale and the optimal scale to vary with factor inten-
sity. However, Moll, in a recent comment on
Grabowski and Belbase, has suggested that the RHF
specification imposes increasing returns to scale and
decreasing returns to scale on the smallest and larg-
est sample firms, respectively.1 He also indicates
that the mean firm size experiences constant returns
to scale and that, for the RHF specification em-
ployed, the effect of factor intensities on optimum
size and returns to scale is dominated by the effect
of output on scale, resulting in decreasing returns for
the largest firms. Grabowski, in reply, correctly re-
inforces that conceptually, scale returns are influ-
enced by both factor intensities and the level of
output. He implicitly argues that the exact nature of
economies of scale for any production technology is
an empirical issue. He also provides empirical evi-
dence demonstrating that the mean firm size is not
characterized by constant returns to scale and the
presence of increasing returns for large firms. Be-
cause of the importance of economies of scale in the
U.S. agricultural sector, the present analysis further
investigates several of these issues. Here, the sample
is divided into small and large farm size groupings
to provide additional insight into the potential ef-
fects of using the RHF to identify the magnitude and
composition of inefficiency.
DATA AND METHODOLOGY
The data come from farms in central Illinois that
keep production, income, and cost records with the
Illinois Farm Business Farm Management (FBFM)
record keeping service. To address the questions
associated with single-year efficiency measurement
and limited homogeneity of farms, a 6-year (1982-
1987) sample of records for 170 “exclusive” cash
grain farms was used. Normally, FBFM defines a
grain farm as one in which the value of feed fed is
less than 40 percent of the crop returns and where
the value of feed fed to dairy or poultry is not more
than one-sixth of the crop returns. The exclusive
grain farms used in this analysis were ones in which
less than 1 percent of the gross value of farm pro-
duction was from livestock sales. In addition, FBFM
classifies farms by a soil productivity rating (SPR).
Only farms with an SPR of 90 or above (on a scale
from 1 to 100) were included in this study. In this
way, a more homogeneous group of grain farms was
examined than in the Bymes or Aly studies.2 More-
over, the sample examined here included farms
which were relatively uniform in crop mix—primar-
ily in com and soybeans.3 By controlling for sample
homogeneity, efficiency measures could more effec-
tively be estimated.
Following Aly et al., the ray-homothetic function,4
lThis specification of the ray-homothetic function was introduced by Fare and Y∞n.
2These studies use the FBFM definition of a grain farm and, do not, to the author’s knowledge restrict SPR ratings.
3Over the six-year period, the farms allocated on average 44,46,1 and 9 percent of their tillable acreage to com, soybeans,
wheat, and set-aside, respectively.
4Using revenue and cost data to measure technical efficiency assumes that producers face the same input and output prices.
This assumption and the use of revenue for output and/or expenditures for some or all of the inputs to estimate production frontiers
has been used frequently. In addition to the Bymes and Aly studies, see Bagi and Huang; Battese and CoeIli; Bravo-Ureta and
Rieger; Elyasiani and Mehdian; Fare, Grosskopf and Lee; Grabowski and Belbase; Grabowski and Mehdian; Huang and Bagi;
Kalirajan and Flinn; Tauer and Belbase; and Timmer. Using this assumption here seems reasonable given that the farms are located
in a relatively homogenous 15-county area in central Illinois. An analysis of the average com and soybean prices received by these
farms reveals no significant differences (at the 5 percent level) between the mean prices of the 85 most and least efficient farms for
five of the six years examined. The effect of using revenue and cost data which could reflect differences in prices faced by
producers means that measures of inefficiency may incorporate some allocative inefficiency as well (Aly et al.).
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