As in other sectors, absolute measurement of efficiency and productivity
is of great importance in the agricultural sector. If efficiency has not
been achieved in production, detection and correction of the source of
failure would minimize the potential economic loss. For the agricultural
enterprises to realize sustainable production, it is necessary to determine
their efficiency level and the factors affecting efficiency. Data envelopment
analysis comes first among the classical methods used to evaluate the
performance of decision- making units. Efficiency measurement with the
method of data envelopment analysis is widely used in the agricultural
sector as well. The measurement of efficiency, an important indicator
used in the decision-making process, is widely used in production processes
where different inputs and outputs are used together (Zhu, 2000; Sharma
et al., 1999; Rahman, 2003; Tauer, 2001).
Majority of efficiency studies were focused on dairy farms. Baily et
al. (1989) estimated efficiency on a sample of Ecuadorian dairy farms.
They found a positive relationship between enterprises size and technical
efficiency. In contrast to the New England study, medium sized Ecuadorian
farms were found to be as allocatively efficient as large farms. Bravo-Ureta
and Rieger (1991) examined efficiency of a sample of New England dairy
farms, using the Stochastic Frontier Approach and Cobb-Douglas production
function. They found overall economic inefficiencies of on average 30%.
However it was little difference between technical and allocative efficiency.
Mbaga et al. (2003) conducted a study in Canada, based on Cobb-Douglas
type production functions. They reported that the mean herd size was 57.7
animals on Quebec dairy farms and the growth rate was 6.8%. Another important
finding of this research was that DEA allowed for the easy performance
of multiple output calculations on the basis of multiple inputs; it was
found to be superior to the Stochastic Production Frontier analysis method.
Lansink et al. (2002) studied technical efficiency of Finnish farms
using data envelopment analysis. They reported that the conventional livestock
farms had technical efficiency scores of 69%. Although DEA should not
be used for comparison between different studies, since the scores only
measure the relative efficiency within the sample (Coelli et al.,
This study attempts to determine the factors affecting bounded continuous
efficiency scores obtained through logistic regression method, in addition
to the classical efficiency measurement.
THE MODEL AND DATA
Measurement of input and output amounts applied by the decision-making
units of the enterprise for the economic decision is needed for the efficiency
measurement of any production enterprise. This provides information on
the efficiency of the production activities on the basis of a comparison
between inputs and outputs. There are three types of efficiency, which
are total efficiency, technical efficiency and scale efficiency. Technical
efficiency is the success of obtaining maximum output by using the input
composition in the most appropriate way. Technical efficiency allows one
to compare between decision making units in terms of production maximization.
The success of production on the right scale is called as scale efficiency.
Total efficiency is obtained by multiplying technical efficiency and scale
Mathematical basis of DEA dates back Farell (1957) who attempted to find
out benefits of efficiency measurement and its application in practice.
DEA is an efficiency measurement method first developed by Charnes et
al. (1978, 1981) for the purpose of measuring relative efficiency
of economic decision making units which are similar in terms of the products
produced. In most simple terms, DEA is a non-parametric linear programming
technique that measures the distance between the input and output values
to the effective limit. When the relative efficiency of a unit is above
the efficient limit on DEA, it means that the unit is efficient. When
it is below this limit, it means the unit is inefficient (Amiteimoori
and Kordrostami, 2005).
Assume each of I decision making unit consumes m different inputs, to
produce outputs Let xij≥0 denote the inputs i consumed and
yrj≥0 denote the output r produced by decision making unit
j. Assume xij >0 and yrj >0 for some i and
r for all j. Then the problem of DEA can be stated as:
Equation 1 is normalization constraint for each decision
making unit. However, this problem will have infinite number of solutions.
Since for different levels of virtual input, we will have different levels
of virtual output. Thus, by imposing
Charnes et al. (1978) take a representative solution. The problem
becomes maximizing the virtual output given a predetermined level of virtual
input. Then the maximization problem will be:
for all i, r
The solution to the above problem will be vectors Y and X, which will
consist of μr s and vi s and finally z will
be the efficiency score.
The calculated z scores were excepted as a dependent variable in logistic
regression model. Dependent variable is generally integrated to the analysis
in binary form in the logistic regression model which is widely used.
In an alternative use of the logistic regression model, the dependent
variable is continuous, but this alternative offers limited range (Manning,
The logistic regression model offers various virtues. Firstly it is
easily transformed into a simple linear regression and secondly it yields
predicted values within the natural boundaries of dependent variable.
According to classical assumptions, ordinary least squares estimation
of the logit model is also free of the heteroscedasticity problem caused
by the use of using the logistic regression with bounded continuous data
S, which is between zero and unity and which is a function of a vector
of dependent variables and X and some error term, ε, symmetrically
distributed around zero are bounded continuous variables. When we apply
the functional form of the logistic distribution on these variables, we
obtain the following finding:
Then we see that standard transformation then produces the simple linear
This study was conducted at 58 crop farms and 78 dairy farms which were
selected from 6989 enterprises in Aydin-Turkey, by using randomly layer
sampling method based on Eq. 8 (Yamane, 1967):
|| Sample size
||Number of subjects in each layer
||Standard deviation in each layer
||Permitted error amount from the main mass mean d2/z2
d, where z shows the z value on the standard normal distribution table
according to the error rate
Crops produced by the crop farms are fig, olive, cotton, corn and wheat.
Efficiency scores of the enterprises were found with DEA analysis. In
DEA analysis, gross production was accepted as the sole output value.
Four variables were taken as input. First and second input values applied
were the variable costs used in the production. The third one is the labor
used in the production. This includes the household labor and foreign
labor as the value of input man work unit and this labor is assumed to
work 300 days a year. In Man Work Unit, 0.50 coefficient was used for
the age group 7-14; 0.75 coefficient was used for the women and 1.00 coefficient
was used for men in age group 15-49; 0.75 coefficient for the men and
0.50 coefficient for the women in the age group 50 and above. The fourth
input is the monetary value of the production areas for the crop farms
and the monetary value of the
||Summary statistics for the output, inputs and DEA scores
|1 US $ = 1.2732 New Turkish Lira (NTL)
total animal assets for the dairy farms. Definitive statistics concerning
outputs and inputs and DEA scores are shown in Table 1.
At the first stage, efficiency scores of the enterprises were determined
by the output oriented DEA (CCR). At the second stage, Logistic Regression
Model was applied, by considering the efficiency scores obtained from
DEA as the dependent variable in order to determine the effects of the
various explanatory variables on efficiency. The model was used separately
for total efficiency, technical efficiency and scale efficiency.
The DEA scores show the bounded and continuous structure between zero
and unity. Therefore, the analysis of DEA scores was carried out by using
the logistic regression method.
The Eq. 3 was fitted by using the Gretl (Cottrell and
The variables which are thought to explain the efficiency scores in the
model are as follows: age of the producer (X1: year), education
period of the producer (X2: year), experience of the producer
(X3: year), dummy variable (X4: 1 for the milk dairies,
0 for others) and enterprise scale (X5: 1 small scale enterprises,
2: bottom group medium scale enterprises, 3: top medium scale enterprises,
4: large scale enterprises). The model was developed primary for the purpose
of revealing the extent to which the owner of the enterprise, general
features of the enterprise can explain the technical efficiency, scale
efficiency and total efficiency.
RESULTS AND DISCUSSION
Table 1 presents DEA scores of 136 agricultural
enterprises, including 58 crop farms and 78 dairy farms. An analysis of
these scores revealed that the technical efficiency was 70%, scale efficiency
was 85% and total efficiency was 60% among the enterprises. According
to these scores, it is necessary to reveal the factors affecting the technical
efficiency in order to increase technical efficiency. For this purpose,
estimations concerning to what extent features of the farm owner, scale
of the enterprise affect the efficiency level of the crop farms and dairy
farms are shown in Table 2. Findings of the logistic
regression analysis indicate that the model explains the total efficiency
by 60%. The extent to which the model can explain technical and scale
efficiency is very low. Total efficiency level in the dairy farms was
significantly higher than the crop farms. In addition, the finding that
efficiency level decreases while enterprise scale increases was also found
statistically significant. It is consistent with previous studies (Bravo-Ureta
and Rieger, 1991; Tauer, 2001; Binici et al., 2006).
||The results of logistic regression for efficiencies
|(t-statistics are in the parenthesis.) *: p<0.05,
**: p<0.01, ***: p<0.001
These findings indicate that conventional dummy variables such as
age, education end experience do not constitute significant factors in
explaining level of efficiency. The findings also reveal that small scale
enterprises display a better performance than the large scale enterprises
in terms of utilizing the resources. It is recommended that dairy production
should be included in the production activity for the purpose of increasing
efficiency of this enterprise in the region, since type of enterprises
favors dairy production in terms of efficiency level.
I sincerely appreciate the help of our colleagues Altug Ozden and
Suleyman Nizam during the field research.