The name is absent

Table 3. Regression Results of the Estimation of
the Ray-Homothetic Revenue Function
for 170 Central Illinois Grain Farms, 6-
year Average Data

* Significant at the 1 percent confidence level.

scale inefficiency each year. Aly et al. find a 0.58
total efficiency ratio for their sample of 88 south-
central Illinois grain farms from 1982 data. It was
anticipated that the more uniform sample of exclu-
sive grain farms utilized in this analysis would pro-
vide higher total efficiency ratios. However, the
efficiency measurement for 1982 in this analysis is
0.52, lower than that of Aly et al. Regardless, it is
clear from Table 2 that the measurement of farm firm
efficiency is dependent upon the time period ana-
lyzed.⁹

Table 2 also provides the aggregate results. The
estimated models fit as well or better than the yearly
regression models with R²s in the 0.90-0.92 range
and all estimated coefficients significant at the 1
percent confidence level. In all but one instance
(1984-1985), the total efficiency ratios of the aver-
aged time periods are equal to or higher than those
of any of the associated individual time periods. This
suggests that in specific years farms may be further
away from the frontier.

When farm data are averaged over the 6-year
period, the total efficiency ratio is found to be 0.65,
higher than any individual year’s estimate and also
higher than any 3-year average estimate. When com-
pared with 2-year average data estimates, it is found
to be lower than only the estimate from the 1982-
1983 period of 0.67. It appears that, on balance,
averaging the data when calculating the efficiency
of a sample of farms using a frontier technique
increases efficiency measures by reducing the ef-
fects of specific annual occurrences. In addition,
these results indicate that using averaged expendi-
ture and revenue data to measure productive effi-
ciency may provide a more effective evaluation by
accounting for the effects of cash vs. accrual meas-
urement errors and the benefits of crop rotation
practices.¹⁰

Efficiency, Farm Size, and Scale Implications

The degree to which efficiency differs by farm size
and total revenue is next examined. For the 6-year
average data (the last line in Table 2), individual
farm estimates of potential and constant returns to
scale revenue are classified by number of tillable
acres and level of actual revenue. Table 4 presents
these results.

As farm size increases when measured either by
acreage or actual revenue, total efficiency ratios
initially increase and then appear to stabilize. In
terms of farm size, the 400-700 acre range is the
point where the total efficiency ratio levels off.¹¹
This size class contains the largest component of the
sample and may be considered to represent single-
family grain farms. Examination of the individual
years and alternative aggregate groupings reveals a
similar pattern. However, in two of the six years, the
total efficiency measure declines once farm size
exceeds 1000 acres.

The composition of the inefficiency changes sys-
tematically; as farm size increases, pure technical

⁹Duncarfs Multiple Range and Fisher’s Least Significant Difference Tests were conducted upon the pure technical and total
efficiency ratios (at the 5 percent level). For the pure technical efficiency ratio, the mean in 1985 was found to he significantly
higher than the means of 1983, 1986 and 1987, which were in turn found to be significantly higher than the means of 1982 and 1984
data. For the total efficiency ratio, the rankings are 1985 > 1983,1986 and 1987 > 1982 > 1984, where “>” denotes significance of
difference between means.

¹⁰For a more careful examination of this result, the “within” estimator (Schmidt and Sickles; Seale) was applied to the panel
data. The results of this procedure indicate that the firms experienced $90,250 of pure technical inefficiency on average over the
six-year period. This result is very similar to the amount of pure technical inefficiency estimated in four (1983,1985, 1986, 1987) of
the six single-year estimations. This suggests that the use of a panel data estimation procedure alone may not be sufficient to
account for some of the problems associated with using a single year’s revenue and expenditure data to assess productive efficiency.
Moreover, the firm efficiency estimates calculated using the within estimator are only consistent as T → ∞, whereas in this analysis
T = 6.

¹¹The Tukey multiple-comparison approach was used to test for significant differences in the means of the total efficiency ratio
of farms classified by acreage. The results indicate that the mean total efficiency ratio of farms with less than 400 acres was
significantly different (at the 5 percent level) from the mean efficiency ratios of all other size classes. No other significant
differences in means were found.

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