The name is absent

livestock products, and value added of
the livestock, in dollars, per farm

L = land operated in acres, per farm. It in-
cludes the rented-in area and excludes
the rented-out area from the area
owned.

N = number of labor hours used per annum
on individual farms; this includes fam-
ily labor and hired labor, if any.

K = the dollar value of the flow of capital
services from farm machinery and
equipment. Included are annual depre-
ciation charges, repair, and operating
expenses (i.e., gas, oil, etc.).

F = the dollar value of fertilizer, lime, pes-
ticides, and herbicides, etc.

XL = feed, fodder, and veterinary expendi-

TABLE 1. OLS Estimates of Cobb-Douglas Pro-
duction Functions for Selected Full-Time and
Part-time Farms in West Tennessee^a

Figures in the parentheses are the estimated t-ratios

^a the output elasticities for the part-time farms are given by
the α₁^,s, and the corresponding output elasticities for the full-
time farms can be calculated as the sum of the α₁^,s and B₁^,s.
The associated t-ratios can be estimated as: t-ratio (α,+B₁) =
(o⅛+B₁)∕{Var(α₁) + Var(B₁) + 2 Cov t<⅛_i,B₁)}'^zi

DW = Durbin-Watson Statistic, SSR = Sum of Squared
Residuals

SER = Standard Error of the Regression, n = the number
of observations

R. S. = Returns to scale, sum of the output elasticities of all
inputs.

tures, and other miscellaneous ex-
penses, in dollars, per farm

u = a random disturbance term that is as-
sumed to be normally distributed with
mean zero (Eu=O), and finite variance
(Eu²=σ²)

D = a dummy variable, zero for part-time
farms, and unity for full-time farms

In the first step, equation (1) was estimated in
its original form, using OLS. But in the final
analysis, only statistically dummy variables were
included, along with the conventional inputs.

RESULTS

Technical Efficiency

The results are presented in Table 1. These
results show that part-time and full-time farm
groups are represented by the factor-biased pro-
duction function. More specifically, these results
show that the output elasticities of capital (K),
fertilizer (F), and expenses on livestock (XL) are
significantly different for the two groups of
farms.⁵ Therefore, an estimation of the pooled
sample of the part-time and full-time farms will
give misleading results.

The next logical step would be to determine
whether the two groups of farms make equally
efficient allocation of the factors of production.
However, a rigorous comparison of the alloca-
tive efficiencies of any two groups of farms re-
quire that they are: (1) characterized by constant
returns-to-scale, (2) represented by the same or
neutral technologies, and (3) facing the same con-
figuration of input and output prices. But the re-
sults in Table 2 show that both groups of farms
have coefficients of returns-to-scale that are
slightly less than unity. However, the difference
is not significant at 5-percent level, and, hence,
the hypothesis of constant returns-to-scale can-
not be rejected. The data have been collected
from two contiguous counties and, thus, there is
very little chance that the two groups may face
different configuration of input and output
prices. On the other hand, the results in Table 1
show that the two groups of farms are repre-
sented by two separate factor-biased production
functions. Therefore, our results will reflect both
technical and allocative efficiencies and not the
latter alone.

Allocative Efficiency

The tests of allocative efficiency are performed
by estimating the following equations for the
Cobb-Douglas production function:

^s This interpretation is based on the results of all farms (pooled sample) in Column 1 of Table 1. There are two methods Oftesting the equality between sets Ofcoefficients in
two linear regressions, one is the so-called Chow Test (Chow, I960), and the other is the use of the Dummy Variables (Bagi; Maddala; Gujarati). The Chow Test is quite
sensitive even to a mild degree Ofheteroscedasticity and multicollinearity. The Dummy Variable approach provides all information necessary to test the equality between sets
of coefficients in two linear regressions in one run; in Chow’s approach, one must run three different regressions (Bagi). Therefore, we have used the Dummy Variable
approach, and the results are given in Column 1 of Table 1. (Columns 2 and 3 are presented to reinforce the validity of the results of the Dummy Variable approach). In the
Dummy Variable approach, a significant coefficient of the interaction between a conventional input and the Dummy Variable (i.e., X_i D) is proof in itself that the coefficient
of X₁ is significantly different in the two groups.

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