For all agricultural sectors, achieving a high level of efficiency is an important
task. Cattle raising has been proven as a main resource to supply meat in Iranian
agricultural industry. The meat consumption in Iran is evaluated to be about
12 kg per person and approximately, 65244 tons were imported in 2007. One of
the most important ways to become free of need of meat in developing countries
is the development of an efficient farm and the improvement of an inefficient
farm (IRICA, 2009).
In the last two decades, several agricultural policies in Iran have attempted to improve the performance of this industry, but none of these policies were scientific.
Due to the arguments presented above, it is important to assess the efficiency of Iranian Caspian cattle feedlot farms.
As we know, the technical efficiency of a farm measures its success in producing maximum outputs from a given set of input. As is well established in the literature, productivity growth can be decomposed into Technological Change (TC) and Technical Efficiency (TE). This decomposition makes it possible to study the sources of productivity growth from different points of view. Specifically, TE can be interpreted as a relative measure of managerial ability for a given technology, while TC evaluates the effect in productivity from the adoption of new production practices. In other words, gains in TE are derived from improvements in decision-making, which in turn are related to a host of variables including knowledge, experience and education. By contrast, TC relates to investments in research and technology.
The purpose of this study is to analysis the technical efficiency in Caspian cattle feedlot farms in Iran by using parametric and nonparametric techniques such as DEA, Data Frontier Analysis (DFA) and Stochastic Frontier Analysis (SFA).
Data envelopment analysis (DEA) is a nonparametric technique for measuring
and evaluating the relative efficiencies of decision making units (DMUs). Since
the pioneering research of Charnes et al. (1979),
DEA has demonstrated to be an effective technique for measuring the relative
efficiency of a set of DMUs which utilize the same inputs to produce the same
The aims of this study is thus to evaluate the technical efficiency in Caspian cattle feedlot farms In Iran. A comparison of DEA, DFA and SFA results is put forwarded.
Data Envelopment Analysis (DEA), introduced by Charnes
et al. (1979), provides a nonparametric methodology for evaluation
the relative efficiency of each of a set of comparable decision making units
(DMUs), relative to one another. The definition of a DMU is generic and DMUs
can be in business firms and others.
In measuring TE, different methodologies and strategies have been proposed
and considerable controversy has surrounded the choice and merits of a specific
methodology and the impact of such choice on the ensuing analysis. Wadud
and White (2000) indicate that in most empirical studies the selection of
the methodology used to measure of TE is arbitrary and mainly based on the objective
of the study, the data variable and the personal preference of the researcher.
In Cook and Green (2005), the DEA technique was used
to evaluate the operational efficiency of a set of electric power plants and
of the individual power units that make up those plants.
Lin et al. (2009) have used the DEA technique
to evaluate the operating efficiency of each branches of the case bank in 2006
in an attempt to have more objective and impartial measuring indices for appraising
the operating performances of branches and proposed the suggestions for each
management DMUs while providing for head quarter management unit to allocate
internal objectives to branches, branches operating advantages and disadvantages
can be known.
Erbetta and Rappuoli (2008) applied the DEA technique
to determine the optimal scale in the Italian gas distribution industry. Stochastic
Frontier Analysis (SFA) and Data Envelope Analysis (DEA) are introduced to measure
and compare the technical efficiency scores for 79 forest and paper companies
by Lee (2005). They suggested that using only one of these
methods to improve efficiency may cause incorrect measurement of increase output
or reduce input since each of these approaches has some inherent limitations.
Before any correctional improvements are taken, the stability of the technical
efficiency estimates from a parametric (or nonparametric) method should be evaluated
by comparing them against those found using the nonparametric (or parametric)
This type of study can be found in the sectors of public education by Chakraborty
et al. (2001), banks by Kohers et al.
(2000) and public schools by Ruggiero and Vitaliano
(1999) and Hjalmarsson et al. (1996).
AN INTRODUCTION TO DEA, DFA AND SFA DEA efficiency analysis: To describe the DEA efficiency measurement, let there are n DUMs and the performance of each DMU is characterized by a production process of m inputs (xij : i = 1,...,m) to yields s outputs (yri : r = l,...,s). The ratio DEA model also known as the CCR model, measures the efficiency of DMUo as the maximum of the ratio of its weighted outputs to its weighted inputs as:
where, the maximum is sought subject to the conditions that this ratio does
not exceed one for any DMUj and all the input and output weights
are positive. To estimate the DEA efficiency of DMUo, we solve the
following DEA model (Charnes et al., 1979):
where, ε>0 is a non-archimedean construct. This linear fractional programming
problem can be reduced to a non-ratio format in the usual manner of Charnes
and Cooper (1962). Specifically, make the transformation
Then Eq. 1 can be expressed in the form:
This model is a Constant Returns to Scale (CRS) program and assumes that all
input/output data are known exactly and all produced outputs are perfect and
complete. The efficiency ratio θo ranges between zero and one,
with DMUo being considered relatively efficient if it receives a
score of one. From a managerial perspective, this model delivers assessments
and targets with an output maximization orientation.
SFA (stochastic frontier approach): The stochastic frontier production
function was independently proposed by Aigner et al.
(1977) and Meeusen and Van den Broeck (1977). The
original specification involves a production function specified for cross-sectional
data which has an error term which is comprised of two components, one to account
for random effects and another to account for technical inefficiency. This model
can be expressed in the following form:
where, Yi is the production (or the logarithm of the production)
of the i-th firm, Xi is a kx1 vector of (transformations of the)
input quantities of t he i-th firm, β is an vector of unknown parameters,
εi s are random errors with N(0, σ2V), which
are associated with random factors such as measurement errors in production
and independent of the Ui, which are non-negative random variables
which are assumed to account for technical inefficiency in production and are
often assumed to be symmetric independently distributed as N(0, σ2,U)
random variables and independent of Ui. This original specification
has been used in a vast number of empirical applications over the past two decades.
A number of comprehensive reviews of this literature are available, such as
Forsund et al. (1980), Schmidt
(1986), Bauer (1990) and Greene
DFA (deterministic frontier approach): For DFA analysis, we estimated Cobb-Douglas production function by the Ordinary Least Square (OLS) method. In this method, the differences between actual production and Frontier Production Attributed to management factors. The Deterministic Frontier Production function was expressed in the following forms:
where, yi is output of farm j; j; Xij is input i that
farm j be used. βi is the OLS estimated coefficient of input
i (the elasticity of input i). εj is representation of technical
efficiency of farm j.
estimated production of farm j that is greater than or equal to its actual
production (ln yj). Only in farms that having 100% technical efficiency,
In = In yi. So we solve
Then technical efficiency is determined as:
METHODOLOGY AND DATA DESCRIPTION
This study utilizes DEA as it is an approach that can easily model slacks,
even though there exists some literature on the separate estimation of technical
and allocative inefficiencies using stochastic frontiers Kumbhakar
and Lovell (2000), Kumbhakar and Tsionas (2004).
DEA studies, however, do not explicitly account for slack variables in the relative
efficiency analysis. As Fried et al. (1993) point
out," The solution to DEA problem yields the Farrell (1957)
radial measure of technical efficiency plus additional non-radial input slacks
and output surpluses. In typical DEA studies, slacks and surpluses are neglected
at worst and relegated to the background at best. Such input and output slacks
are essentially associated with the violation of neoclassical assumption. If
we take the standard input-oriented DEA approach, for example, input slacks
would be associated with the assumption of strong or free disposability of inputs.
Hence, units with extensive usage of some inputs would be deemed to be efficient
according to standard Banker et al. (1984). If
slacks were incorporated into the relative efficiency analysis, however, such
units could actually be found to be inefficient.
For the reasons outlined above, therefore, we feel it is appropriate to use
the Slack-Based Measure (SBM) of Tone (2001). This SBM
approach specifically incorporates slacks in the objective function. To describe
the SBM model of Tone, let there are n DMUs and the performance of each DMU
is characterized by a production process of m inputs(xij : i = 1,...,m)
to yields s outputs (xij : i = 1,...,s):
The optimal solution is when e0 = 1 and hence a DMU will have zero
input and output slacks and be fully efficient on the frontier. We also have
used Stochastic Frontier Analysis (SFA) and frontier analysis to evaluate the
cattle feedlot farms. The sample consisted of around 70 Iranian Caspian cattle
feedlot farms. The data for this analysis are derived from operations during
2007 and 2008.
The raw data are reported in Table 1. We use six variables from the data set as inputs and outputs. Inputs include number of calve per farm (x1), number of labors/ days/hours (x2), total metabolizable energy intake (Mcal) (x3), total crude protein intake (kg) (x4) and total cost of hygiene- treatment of calve (Rials) (x5).
The unique output is total live weigh gain of calve per farm (kg) (y).
Details of inputs and outputs are defined below:
||Calve per farm: Number of calve per farm
||Labors: Number of labors
||Metabolizable energy intake
||Crude protein intake
||Cost of hygiene- treatment of calve
||Live weight gain of calve per farm
Table 2 presents the estimation results of the cost and technical frontiers, as the table indicates, 11 farms are efficient in DEA. However, we note that except for farm 3, all of the other farms are inefficient in DEA and DFA approaches.
We also have calculated the correlation between the mean of technical efficiencies calculated in different methods. The results are listed in Table 3, as we can see there is a significant correlation in different methods. The maximum correlation is DFA and SFA, while the minimum one is in DEA and DFA. It is to be noted that DEA is a nonparametric approach, while DFA is a parametric approach. Efficiency intervals in three methods DFA, DEA and SFA are, respectively (0.15 , 1), (0.2 , 1) and (0.183 , 1). As we can see, farm 3 is the top-ranked farm and farm 13 is the low-ranked in three methods.
Table 4 presents Descriptive Statistics of technical efficiency, means of technical efficiency in DFA(0. 6910) is the least and significantly different with SFA(0. 6910) and DEA(0. 7221) Methods(p<0.01).
||Variables and raw data get as inputs(x1
x5) and output(y)
||Technical efficiency estimated by DFA, SFA and DEA methods
|**Correlation is significant at the 0.01 level (2-tailed)
||Descriptive statistics of technical efficiency
|*Difference is significant (p<0.01), (cal F = 6.166), (N
Efficiency scores in this study were estimated using the computer programs,
DEAP Version 2.1 (Coelli, 1996), FRONTIER Version 4.1
and SPSS Statistics 17.0.
This study uses the DEA, DFA and SFA to evaluate the operating efficiency cattle feedlot farms. The paper has taken 70 farms in Iran in 2007-2008 as the research subject and has used DEA, DFA and SFA to evaluate the operating performances of these farms. The results indicated that 11 farms are efficient in DEA technique. However, in DFA and SFA, the number of efficient farms are 1 and 0, respectively. Moreover, the average technical efficiency of farms in DFA, SFA and DEA were respectively, 0.5986, 0.6910 and 0.7221.