SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS DECEMBER 1991
EFFICIENCY MEASURES USING THE RAY-HOMOTHETIC
FUNCTION: A MULTIPERIOD ANALYSIS
David L. Neff, Philip Garcia, and Robert H. Hornbaker
Abstract
Recent investigations have provided mixed as-
sessments of farm firm efficiency. This analysis
examined the efficiency of a homogeneous sample
of central Illinois grain farms over a six-year period.
A best-practice frontier was constructed using the
ray-homothetic function, which allowed optimal
farm output to vary with factor intensity. Efficiency
measures were found to increase with temporal ag-
gregation. The ray-homothetic approach was found
to attribute high scale inefficiencies to larger sample
farms in cases where the factor shares did not vary
appreciably across farms. The findings suggest that
policy recommendations regarding farm efficiency
must be made with care.
Key words: technical efficiency, ray-homothetic
function, temporal aggregation,
Illinois grain farms
Firm efficiency has long been an area of interest in
the investigation of farm operations. Its absence or
presence can have important implications for issues
related to economic survival, the size distribution of
farms, technological adoption, and the overall level
of input usage in the agricultural sector. These issues
are of critical importance in the current public and
private dialogue about the continued existence of
medium-sized family farms and potential viability
of limited input agriculture.
Recent investigations in predominantly grain-pro-
ducing areas have produced somewhat mixed as-
sessments of farm firm efficiency. Bymes et al.,
employing a linear programming approach to assess
the efficiency of 107 south-central Illinois grain
farms in 1980, found that farms were producing only
four percent below their efficient level. Overall ef-
ficiency was relatively consistent across size distri-
bution, except for farms of less than 100 acres. Aly
et al. Constracted a best-practice frontier using a
ray-homothetic production function which permits
returns to scale to vary with output. Pure technical,
scale, and total efficiency were assessed using 1982
records from 88 south-central Illinois farms. Farms
were found to be producing roughly 42 percent
below their efficient levels—a surprisingly low re-
sult considering that their sample contained farms
from the same three-county area used in the Bymes
et al. study. Aly et al. further concluded that overall
efficiency increases with larger farm size and gross
revenue categories.
Various factors might explain the differences in
findings. Each of the studies focused on a particular
year, which means that the results may be condi-
tioned by specific temporal events. In agriculture,
weather and its variability can have dramatic effects
on production, and this can, clearly influence meas-
urements of efficiency. Another possible explana-
tion may reside in the limited homogeneity of the
samples. Differences in the definition of grain farms,
output mix, and soil quality can confound the meas-
urement of efficiency in agricultural settings. Fi-
nally, the differences in the previous results may be
a function of the different methodologies employed.
Bymes et al. estimated a piecewise-linear best prac-
tice frontier using linear programming whereas Aly
et al. econometrically constructed a smooth frontier
using a ray-homothetic production function and cor-
rected ordinary least squares.
The purpose of this paper was to provide insight
into the mixed assessments of farm firm efficiency.
Here, for various temporal aggregates, the technical
efficiency of a sample of well-defined central Illi-
nois grain farms was examined by employing the
ray-homothetic approach. Time-series, cross-sec-
tion data were used over a six-year period. Measures
of technical efficiency and its components were
generated for various time periods and farm size
classifications.
Temporal units of aggregation (i.e., based on av-
erages of two, three, and six years) were formed to
identify their effect on efficiency measurement us-
ing revenue and expenditure data. As previously
mentioned, weather and its variability may influence
David L. Neff is an Assistant Professor in the Department of Agricultural Economics and Rural Sociology, University of Arkansas
at Fayetteville, and Philip Garcia is a Professor and Robert H. Hombaker is an Associate Professor in the Department of Agricultural
Economics, University of Illinois at Urbana-Champaign. This work was supported by University of Illinois at Urbana-Champaign
Campus Research Board Grant No. 1-2-69943.
Copyright 1991, Southern Agricultural Economics Association.
113